X is a continuous uniform (-9,9) random variable. Define the event B-1 7} (a) What is the conditional PDF?a) fx|B(x) =b) E|X|B =
Answers
Conditional expectation PDF is b) E[X|B] = 0.
How to find conditional PDF?The given information states that X is a continuous uniform random variable with a range (-9, 9). Let's define the event B = {X < -1 or X > 7}. We need to find the conditional PDF and the conditional expectation of X given B.
a) To find the conditional PDF, fx|B(x), we first need to determine the PDF of the uniform distribution and the probability of event B.
For a continuous uniform distribution in the interval (-9, 9), the PDF is given by:
f(x) = 1/(9 - (-9)) = 1/18 for -9 ≤ x ≤ 9, and 0 otherwise.
Next, we calculate the probability of event B, P(B). Since X < -1 and X > 7 are disjoint events, we can find the probability of each event and sum them:
P(B) = P(X < -1) + P(X > 7) = (-1 - (-9))/18 + (9 - 7)/18 = 8/18 + 2/18 = 10/18 = 5/9.
Now, we can find the conditional PDF fx|B(x) by dividing the PDF of the uniform distribution by the probability of event B for the intervals specified by B:
fx|B(x) = f(x) / P(B) = (1/18) / (5/9) = 9/10 for -9 ≤ x < -1 or 7 < x ≤ 9, and 0 otherwise.
b) To find the conditional expectation E[X|B], we'll integrate the product of the conditional PDF and the variable x over the intervals specified by B:
E[X|B] = ∫[-9, -1] (9/10)x dx + ∫[7, 9] (9/10)x dx
= (9/10)[(x²)/2] from -9 to -1 + (9/10)[(x²)/2] from 7 to 9
= (9/20)[-1² - (-9)²] + (9/20)[9² - 7²]
= (9/20)[-80 + 80]
= 0
So, the conditional expectation E[X|B] = 0.
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Related Questions
The graph shows the number of weeks of practice (x) and the number of
shots missed in a free-throw drill (y). The equation of the trend line that best
fits the data is y = -x + 6. Predict the number of missed shots after 8
weeks of practice.
Number of shots missed
pa
89
Weeks of practice
Click here for long
description
Answers
The predicted number of shoots missed after 8 weeks of practice is given as follows:
-2 shots.
How to find the numeric value of a function at a point?To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y = -x + 6.
Hence the predicted value when x = 8 is given as follows:
y = -8 + 6
y = -2.
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The perimeter of the scalene base of a pentagonal right prism is 17, and a lateral edge of the prism measures 10. Find the prism's lateral area.
Answers
The lateral area of the pentagonal prism is = 850
What does a pentagonal prism?A prism with two pentagonal bases and five rectangular sides is called a pentagonal prism. It is a hexagon.
the pentagonal prism has a base that is pentagonal. With seven faces, fifteen edges, and ten vertices, it is a particular kind of heptahedron.
What do you mean by lateral area?All of an object's sides, excluding its base and top, are referred to as its lateral surface (when they exist). The size of the lateral surface is referred to as the lateral surface area. The total surface area, which consists of the lateral surface area along with the areas of the base and top, should be distinguished from this.
According to the given information :base of a pentagonal right prism is = 17
lateral edge of the prism measures = 10
the prism's lateral area = ?
According to the formula :
Area = 5 x base x height
= 5 x 17 x 10
= 850
The lateral area of the pentagonal prism is = 850
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WUOI Monthly salary Maintenance money R10 565 R1200 FIXED EXPEI Loan repayment R5400 School Fees R600 Lunch Money R300 VARIABLE EXPENSES Electricity R500 Transport R480 Food R2100 Clothing R500 Cellphone airtime R375 Compare Lebogo's total income with her total expenditure to justify if she is in good financial status or not.
Answers
Answer:
go check my i-n-s-t-a-g-r-a-m please
Step-by-step explanation:
and follow me
simohamed647
If t=2t=2, then 3t-4=23t−4=2.
True
False
Answers
Answer:
false
Step-by-step explanation:
Answer:
TRUEE
Step-by-step explanation:
If t = 2
\(3t - 4 = 2\)
\(3(2) - 4 = 2\)
\(6 - 4 = 2\)
\(2 = 2\)
93 is what percent of 300
Answers
\(\sf \longmapsto \: \dfrac{93}{300} \)
\(\sf \longmapsto \: \dfrac{93}{300} \times x\)
\(\sf \longmapsto \: \dfrac{93}{300} \times 100\)
\(\sf \longmapsto \cancel\dfrac{93}{300} \times \ \cancel\dfrac{100}{100}\)
\(\sf \longmapsto \: \dfrac{31}{100} \)
\(\sf \longmapsto \: 31\%\)
Simplify to create an equivalent expression.
3
�
+
2
(
−
2
�
−
1
)
3n+2(−2n−1)
Answers
Answer:
C. \(-n - 2\)
Step-by-step explanation:
Given expression is \(3n+2(-2n-1)\)
Now we need to simplify \(3n+2(-2n-1)\) to create an equivalent expression then match with correct choice from the given choices:
A. \(-n + 2\)
B. \(n + 2\)
C. \(-n - 2\)
D. \(n - 2\)
\(3n+2(-2n-1)\)
\(=3n+2(-2n-1)\)
\(=3n+-4n-2\)
\(=-n-2\)
Hence correct choice is C. \(\bold{-n - 2}\)
If ΔABC is an equilateral triangle with, AB = 2x + 17, BC = 6x - 19, AC = 4x-1, find x and the measure of each side
Answers
Answer:
\(x=9, AB=BC=AC=35\)
Step-by-step explanation:
Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that \(AB=BC=AC\). We are given the lengths of all 3 sides in terms of \(x\), but we only need to set two of them equal to each other to solve for \(x\). Let's use \(AB\) and \(BC\) to solve for \(x\). We know that \(AB=BC\), \(AB=2x+17\), and \(BC=6x-19\). Therefore, we can write the following equation to solve for
\(AB=BC\\2x+17=6x-19\) (Substitute given values into equation)
Solving for \(x\), we get:
\(2x+17=6x-19\\2x+17-17=6x-19-17\) (Subtract \(17\) from both sides of the equation to isolate constants)
\(2x=6x-36\) (Simplify)
\(2x-6x=6x-36-6x\) (Subtract \(6x\) from both sides of the equation to isolate \(x\))
\(-4x=-36\) (Simplify)
\(\frac{-4x}{-4}=\frac{-36}{-4}\) (Divide both sides of the equation by \(-4\) to get rid of \(x\)'s coefficient)
\(x=9\) (Simplify)
Therefore, \(AB=2x+17=2*9+17=18+17=35\), and \(AB=BC=AC=35\). Hope this helps!
Help anyone can help me do this question,I will mark brainlest.
Answers
Answer:
x = 10
Step-by-step explanation:
From the front view: (base* is actually the height, being longer)
Let length = k and breadth = 2 cm
From the front view:
Height of the triangle =
= length of rectangle - breadth
= k - 2
Given, height = 6cm
Therefore, k - 2 = 6 → k = 8
Length = 8 cm
The base of the triangle is length of the rectangle.
Base = 8 cm
Now, perimeter = 24 cm
=> height + base + hypotenuse = 24 cm
=> 8 + 6 + x = 24 cm
=> x = 10 cm
2):
Perimeter of shape =
= sum of outer boundaries
= breadth + length + length + breadth + x
= 2 + 8 + 8 + 2 + 10
= 30 cm
What is the radius of a hemisphere with a volume of 281,250 2.14 cm^3
Answers
Answer:
:
Answer:the radius would be 88cm
Step-by-step explanation:
radius. r = base circumference. C = volume. V = curved surface area.
What is 3 and 5/8 + 6 and 1/2
Answers
Explanation you have to multiply the 6 1/2 by 4 to get common denominator and then add the two improper fractions which will give you another improper fraction
Factor the polynomial completely
10³ -25r² - 12r + 30
Answers
(5r^2 - 6)(2r - 5)
EXPLANATION
Factor by grouping
(10r^3 - 25r^2) + (-12r + 30)
Factor a GCF
5r^2 (2r - 5) -6 (2r - 5)
Combine groups
(5r^2 - 6)(2r - 5)
CHECK
Use FOIL
First: 5r^2*2r = 10r^3
Outside: 5r^2*-5 = -25r^2
Inside: -6*2r = -12r
Last: -6*-5 = 30
Divide using long division.
(9p2 + 8p3 + 12) ÷ (p + 1)
Answers
Answer:
8p∧2 ± p - 1 ± 13/p ± 1
Step-by-step explanation:
Divide (9p2 + 8p3 + 12) ÷ (p + 1) and it equals 8p∧2 ± p - 1 ± 13/p ± 1
Answer:
8p^2+p-1 with a remainder of 13
Step-by-step explanation:
p+1 divided by 8p^3+9p^2+0p+12
A gardener will use up to 300 square feet for planting flowers and vegetables. He wants the area used for vegetables to be at least four times the area used for flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and y that satisfy these requirements.
Answers
Answer:300
Step-by-step explanation:
Because the total area planted (240 square feet) is going to be composed of an area of flowers (x) and an area of vegetables, you can say x + y ≤ 240 (because he will use UP TO 240 square feet)
Because the area of vegetables will be AT LEAST twice the area of flowers, you can say y ≥ 2x
Please explain in detail the utilization of Thematic Analysis in
a Qualitative Descriptive Study Design.
Answers
Thematic Analysis is a process that is used to analyze the text in research in qualitative research. It aims to find the patterns in the data by examining the contents of the text.
In the Qualitative Descriptive Study Design, thematic analysis is utilized to analyze the data obtained from interviews, observation, or other qualitative methods. This method involves the identification of themes and patterns in the data. It helps the researcher to organize the data, identify patterns, and develop the categories and themes that will be used to describe the findings of the study.
Thematic Analysis is used in Qualitative Descriptive Study Design to provide an in-depth understanding of the research topic. It allows the researcher to capture and analyze the rich and diverse experiences of the participants in the study. In this method, data is collected from the participants, and the researcher analyzes the data by identifying the common themes and patterns that emerge from the data. This process of analysis is done in a systematic and iterative manner until the researcher identifies all the themes that are relevant to the research question.
Thematic analysis is useful in qualitative research because it allows the researcher to identify the themes and patterns in the data that are not explicitly stated by the participants. It helps to identify the underlying meanings of the data and to develop a deeper understanding of the research topic. This method is particularly useful when the researcher is dealing with large volumes of data and wants to identify the key themes and patterns that emerge from the data.
In conclusion, Thematic Analysis is a useful method of analysis in Qualitative Descriptive Study Design. It is used to analyze the data obtained from interviews, observation, or other qualitative methods. This method involves the identification of themes and patterns in the data and helps the researcher to organize the data, identify patterns, and develop the categories and themes that will be used to describe the findings of the study.
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A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?
Answers
The function which represents the cost to drive a car from this agency miles x a day is :
C(x) = 15, if 0 ≤ x ≤ 200
= 15 + 0.05x, if x > 200
Given that,
A car rental agency charges $15 a day for driving a car 200 miles or less.
The function can be written as,
C(x) = 15 if 0 ≤ x ≤ 200
If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.
C(x) = 15 + 0.05x, if x > 200
Hence the correct option is D.
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a 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a box with the maximum volume? enter the area of the square as an exact answer.
Answers
a) To get the maximum volume of the box, we should cut squares with side length of 5.66cm from each corner of the cardboard.
b) The area of each square is 31.96 square cm.
Let's denote the side length of the square that needs to be removed from each corner as "x"
The length of the cardboard box, after removing the squares from each corner, will be
L = 119cm - 2x
Similarly, the width of the cardboard box will be
W = 24cm - 2x
And the height of the cardboard box will be
H = x
To maximize the volume of the box, we need to find the value of "x" that maximizes the expression for the volume of the box, which is given by
V = LWH
Substituting the expressions for L, W, and H in terms of x, we get
V = (119cm - 2x)(24cm - 2x)(x)
Expanding this expression gives
V = 4x^3 - 286x^2 + 2856x
To find the value of "x" that maximizes this expression, we can take the derivative of V with respect to x and set it equal to zero
dV/dx = 12x^2 - 572x + 2856 = 0
Solving for x gives
x = (572 ± sqrt(572^2 - 4(12)(2856)))/(2(12))
x ≈ 5.66cm (ignoring the negative root)
Therefore, to get the maximum volume of the box, we should cut squares with side length of 5.66cm from each corner of the cardboard.
The area of each square is x^2 = 5.66^2 = 31.96 square cm.
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HELP
Find the value of x.
160°
(10x + 50)
Α. 21
Β. 13
Ο Ο
Ο C. 4
Ο D. 11
Answers
Answer:
Hello! answer: 11
Step-by-step explanation:
these are vertical angles meaning they Will equal the same measure so... 10 × 11 = 110 110 + 50 = 160 therefore x = 11 HOPE THAT HELPS!
Which equation has no solution?
O 4(x + 3) + 2x = 6(x + 2)
O 5+2(3 + 2x) = x + 3(x + 1)
O 5(x + 3) + x = 4(x + 3) + 3
O 4 + 6(2 + x) = 2(3x + 8)
Answers
Answer:
The equation which has no solution is 5 + 2(3 + 2x) = x + 3(x + 1) . (see below for work)
Step-by-step explanation:
4(x + 3) + 2x = 6(x + 2)
4x + 12 + 2x = 6(x + 12)
4x + 2x = 6x
6x = 6x
x ∈ ℝ
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3(x + 3)
11 + 4x = x + 3x + 3
11 + 4x = 4x + 3
11 = 3
x ∈ ∅ (CORRECT ANSWER)
5(x + 3) + x = 4(x + 3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 12 + 3
6x + 15 = 4x + 15
6x = 4x
6x - 4x = 0
2x = 0
x = 0
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
4 ÷ 12 = 16
16 = 16
x ∈ ℝ
Hope this helps! :)
find the surface area of that part of the plane that lies inside the elliptic cylinder
Answers
The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.
We are given the two equations are:
10x + 7y + z = 4---------(1)
\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)
equation(1) is written as
z = 4 - 10x - 7y-----------(3)
The surface area is given by the equation:
A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)
compare equation(4) with equation(3) we get the values of ∂f/∂x and
∂f/∂y
∂f/∂x = -10
∂f/∂y = -7
substitute these values in equation(4)
A(S) = ∫∫√[(-10)² + (-7)² + 1]dA
A(S) = ∫∫√[100 + 49 + 1]dA
A(S) = ∫∫√[150]dA
A(S) = √150 ∫∫dA
Where ∫∫dA is the elliptical cylinder
From the general form of an area enclosed by an ellipse with the formula;
comparing x²/a² + y²/b² = 1 with x²/25 + y²/9 = 1, from that we get the values of a and b
a = 5 and b = 3
So, the area of the elliptical cylinder = πab
Thus;
A(S) = √150 × π(5 × 3)
A(S) = 15π√150
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Rational numbers are_____________ natural numbers.
never
sometimes
always
Answers
Answer:
Sometimes
Step-by-step explanation:
This is because not all rational numbers are natural numbers
Answer my question please.
Answer:
sometimes
Why is a natural number expressed as a rational number?Because every rational number of the form
n / 1
is actually the integer n. Which means that every natural number is expressible as a rational number, just by putting a fraction line and denominator 1 under it.
It takes Max three hours to run 30 kilometers. Georges, on the other hand, travels the same distance in 2 hours and 20 minutes. If both are to complete a 15-kilometre race, how long before Max will Georges arrive to the finish line?
Answers
George will arrive 20 minutes before Max
It takes Max 3 hours(180 minutes) to run 30 km .
The rate can be calculated as follows:
rate = 30 / 180 = 1/6 km/ min
George uses 2 hours 20 minutes(140 minutes) to run 30 km.
The rate can be calculated as follows:
rate = 30 / 140 = 3/14 km / min
If both are to complete a 15-kilometre race, Therefore,
Max time will be
1 / 6 = 15 / t
t = 15 × 6
t = 90 minutes
George time will be
3/14 = 15 / t
3t = 210
t = 210 / 3
t = 70 minutes
Time difference = 90 - 70 = 20 minutes
Therefore, George will arrive 20 minutes earlier than Max
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A rental car company is running two specials. Customers can pay $50 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $40 the first day and $8 for every additional day beyond that. Camilla notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Camilla pay in total?
Answers
The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.
EquationCompact car:
Fixed price = $50Additional price per day = $6y = 50 + 6x
Another special:
Fixed price = $40Additional price per day = $8y = 40 + 8x
let
x = number of additional days
50 + 6x = 40 + 8x
collect like terms50 - 40 = 8x - 6x
10 = 2x
Divide both sides by 2x = 10/2
x = 5 days
Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.
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Un concensario de coches rebaja a 16000 un vehiculo que valia 18300 en que porcentaje lo han rebajado?
Answers
As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .
The initial price of the car is set at P = 18300 (units)
The price after lowering drom P becomes A= 16000 (units)
Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.
The formula for calculating percentage change is given as follows,
Change in percentage = [(Change in value)/ ( Initial value) ]*100
⇒Change in percentage = (C/ P)*100
⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)
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PLZ HELP!!!! A grocery store sells pint baskets of strawberries as loss leaders, which means the store is willing to lose money selling them. The store loses $0.17 per pint. How much will the store lose if it sells 3450 pints?
Answers
Answer:
The correct answer is $586.50
Answer:
586.5
Step-by-step explanation:
They lose 0.17 per pint which is 3650 so you have to multiply 3450 x 0.17
You will get 586.5
Choose the slope and y-intercept that
correspond with the graph.
HELPPP!!!!!!
Answers
Answer:
Slope:-1/4 y-int: 3
Step-by-step explanation:
You can you the formula y1-y2/x1-x1 or you can look at it and find out if that makes sense
Mrs. Thomas has $71.00 to purchase bottles of juice for her class. If the bottles of juice cost $3.55 each, how many bottles can she buy? 2 bottles 5 bottles 20 bottles 25 bottles
Answers
Step-by-step Explanation:
$71.00 is the total.
$3.55 is for one bottle.
So you have to divide $71.00 by $3.55, to find out how many she can buy. So,
$71.00/$3.00 = 20.
Mrs. Thomas can buy 20 bottles of juice.
Mrs. Thomas has $71.00 to purchase bottles of juice for her class. If the bottles of juice cost $3.55 each, how many bottles can she buy?
2 bottles
5 bottles
20 bottles
25 bottle
the is c 20 bottles
The temperature in a hot tub is 103° and the room temperature is 75°. The water cools to 90° in 10 minutes. What is the water temperature after 20 minutes? (Round your answer to one decimal place.) After how many minutes will the temperature be 80°? (Round your answer to one decimal place.)
Answers
Answer: 77°
Step-by-step explanation:
103° - 90°= 13°, 13° = 10 min
13°+13°= 26°
103°-26°= 77°
True or False. When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.
Answers
False. When conducting a cluster sample, it is typically preferable to have more heterogeneous clusters with fewer individuals.
Why is this statement false?This is due to the fact that when clusters are diverse, it is crucial to appropriately represent the population by capturing its diversity.
In such situations, the danger of sampling bias is increased by having fewer clusters with more individuals because a larger number of people from a single heterogeneous cluster would not fairly represent the overall community. Incorrect estimates and conclusions may result from this.
Having fewer clusters with more individuals, on the other hand, can assist raise the precision of the estimates when clusters are homogeneous by lowering the variance associated with sampling from a single cluster. In general, to achieve a precise representation of the population and to lessen the chance of sampling bias, the number of clusters and the size of each cluster should be balanced.
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A $45.00 purchace in Iowa totals $47.70 with tax and a $35.00 purchase in tenesse totals $37.35 with tax. Which state has a greater sales tax percentage
Answers
Tennessee has a higher sales tax percentage than Iowa, as the tax added to the $35.00 purchase was 6.0%, while the tax added to the $45.00 purchase in Iowa was 6.0%.
In Iowa, the sales tax rate is 6.0%, meaning that for every dollar spent, six cents are added as tax. So, for a $45.00 purchase, the tax added would be $2.70 (6% of $45.00). Therefore, the total amount paid would be $47.70 ($45.00 + $2.70).
Similarly, in Tennessee, the sales tax rate is also 6.0%, meaning that for every dollar spent, six cents are added as tax. For a $35.00 purchase, the tax added would be $2.10 (6% of $35.00). Therefore, the total amount paid would be $37.35 ($35.00 + $2.10).
Comparing the two, we can see that Tennessee has a higher sales tax percentage, as the same 6% tax rate results in a higher amount of tax added to the purchase price.
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Tennessee has a higher sales tax percentage than Iowa, as the tax added to the $35.00 purchase was 6.0%, while the tax added to the $45.00 purchase in Iowa was 6.0%.
In Iowa, the sales tax rate is 6.0%, meaning that for every dollar spent, six cents are added as tax. So, for a $45.00 purchase, the tax added would be $2.70 (6% of $45.00). Therefore, the total amount paid would be $47.70 ($45.00 + $2.70).
Similarly, in Tennessee, the sales tax rate is also 6.0%, meaning that for every dollar spent, six cents are added as tax. For a $35.00 purchase, the tax added would be $2.10 (6% of $35.00). Therefore, the total amount paid would be $37.35 ($35.00 + $2.10).
Comparing the two, we can see that Tennessee has a higher sales tax percentage, as the same 6% tax rate results in a higher amount of tax added to the purchase price.
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Express the ratio below in its simplest form
12:6
Answers
Answer:
12/6 simplified to lowest terms is 2/1.
Step-by-step explanation:
Divide both the numerator and denominator by the HCF
12 ÷ 6
6 ÷ 6
Reduced fraction:
12/6 simplified to lowest terms is 2/1.
Answer: 2:1
Step-by-step explanation:
12:6
Both left and right can be divided by 6, like a fraction, reduce.
= 2:1