The random variables X and Y are jointly continuous, with a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,otherwise, where c is a normalizing constant. For x∈[0,0.5] , the conditional PDF fX|Y(x|0.5) is of the form axb . Find a and b .
Answers
Answer:
The value of a and b are 8 and 1 respectively
Step-by-step explanation:
\(f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 , \text{otherwise}\end{matrix}\right.\)
\(\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1\\\\c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1\\\\\frac{c}{2}\int_{0}^{1}x\left ( 1-y^2\right )\text{dx}=1\\\\\frac{c}{2}\int_{0}^{1}(x-x^3)\text{dx}=1\\\\\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1\\\\\frac{c}{2}\left [ \frac{1}{2}-\frac{1}{4} \right ]=1\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1\\\\c=8\)
Conditional pdf of \(f_{x,y}(x|0.5)\)
\(f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}\)
Normalizing pdf of 1
\(f_{y}y=\int_{0}^{y} 8yx \text{dx}\)
\(f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\\f_{y}y=4y(y^2)\\f_{y}y=4y^3\\f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}=\frac{2x}{0.25}=8x\)
We are given that PDF \(f_{x|y}(x|0.5)\) is of the form \(ax^b\)
So, on comparing 8x with \(ax^b\)
So, a = 8 , b = 1
So, the value of a and b are 8 and 1 respectively
The resulting value of a and b given the conditional PDF of fX|Y(x|0.5) is mathematically given as
a = 8 , b = 1 .
What are the values of a and b?Question Parameters:
a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,
For x∈[0,0.5]
the conditional PDF fX|Y(x|0.5)
Generally, the equation for the function of (x,y) is mathematically given as
\(f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 ,\end{matrix}\right.\)
Therefore
\(\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1\)
\(c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1\)
\(\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1\)
\(\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1\)
C=8
Where, the conditional PDF fX|Y(x|0.5)
\(f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}\)
We have
\(f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\\)
\(f_{y}y=4y^3\)
\(f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}\)
f_{x|y}(x|0.5)=8x
In conclusion. with the pdf in the form of ax^2
8x comparing ax^b
The value of a = 8 , b = 1 .
Read more about Arithmetic
https://brainly.com/question/22568180
Related Questions
please help me!
pls?
Answers
Answer:
19-12=7
hope this will help
what is 30% of 70?
I am confused
Answers
Answer:
21
Step-by-step explanation:
Answer:
Its 21
Step-by-step explanation:
In x= 2.1
A. x = 5.71
O B. X= 8.17
C. X= 7,51
O D. X = 0.74
Answers
Answer:
5.71
Step-by-step explanation:
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).
The paper scissors pencils stickers and paint belong on the top shelf of the craft closet.
Select the best sentence that demonstrates the needed corrections for the sentence.
Group of answer choices
The paper scissors pencils stickers, and paint belong on the top shelf of the craft closet.
The paper scissors, pencils, stickers and paint belong on the top shelf of the craft closet.
The paper, scissors, pencils, stickers, and paint belong on the top shelf of the craft closet.
The paper, scissors, pencils, stickers and, paint belong on the top shelf of the craft closet.
Answers
Explanation: When you are listing items, you need to place a comma in between them. The comma in between the “stickers” and “and” is the Oxford comma. When you lost multiple items, you need a comma after the word before “and”.
im pretty sure what the other guy said is right
find the value of x in the figure shown.
(Hint: the sum of angle measures in any triangle is 180
2x-10
(4x-80)
4x-10
Answers
Answer:
28
Step-by-step explanation:
2x +4x +4x-10 -80-10
10x-100=180
10x=180+100
10x=280
10x/10=280/10
x=28
If m = 2, and k = 3, what is k2 + m?
Answers
3²+2 = 11
hope it helps
Answer:
11
Step-by-step explanation:
3 squared is 9
squared just means multiplied by itself
which would be 3×3
and then add 2
which is 11
3. An investor plans to invest $500/year and expects to get a 10.5% return. If the investor makes these contributions at the end of the next 20 years, what is the present value (PV) of this investment today?
Answers
The present value (PV) of the investment today is approximately $2,965.05.
To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.
The formula for the present value of an annuity is given by:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.
Let's plug in these values into the formula and calculate the present value (PV):
PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]
Using a calculator, we can evaluate the expression inside the brackets:
PV = $500 * [(1 - 0.376889) / 0.105]
Simplifying further:
PV = $500 * [0.623111 / 0.105]
PV = $500 * 5.930105
PV = $2,965.05
Therefore, the present value (PV) of the investment today is approximately $2,965.05.
for such more question on present value
https://brainly.com/question/28256489
#SPJ8
2 points
21. Colin bought a car for $32,555. The value of the car depreciates by the same amount
each
year.
After 10 years, his car is now worth $18,725. What is the rate of depreciation?
Answers
Answer:
The Rate is 1,383!
Step-by-step explanation:
1st)32,555-18,725=13,830
2nd)13,830/10=1,383.
HOPE THIS HELPS!!!!!!!!!!!!!
Given the function, f(x) = 2x 4 + 2x2 – 4x, what is the maximum number of turning points the graph can have?
Answers
Step-by-step explanation: f ( x ) = x4 - x3 - 4x2 + 4x
749/d * d/749 = 1
d=?
Answers
Answer:
D=1
Step-by-step explanation:
1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1
Answer:
I honestly don't know but I think its all real numbers but not zero
Step-by-step explanation:
Solve for angles x and y in the triangle below. Round your angle to the nearest whole degree.
Solve for both x and y
Answers
\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)
Make sure your calculator is in Degree mode.
Find the distance between A and B
Answers
The measure of the distance between point A (-5,3) and point B (5,-3) is \(2\sqrt{34}\) units.
What is the measure of the distance between point A and point B?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
From the graph:
Point A (-5,3)
x₁ = -5y₁ = 3Point B (5,-3)
x₂ = 5y₂ = -3Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 5 - (-5) )² + ( -3 - 3 )² )
D = √( ( 5 + 5 )² + ( -3 - 3 )² )
D = √( ( 10 )² + ( -6 )² )
D = √( 100 + 36 )
D = √( 136 )
D = \(2\sqrt{34}\)
Therefore, the distance between the two points is \(2\sqrt{34}\) units.
Option D) \(2\sqrt{34}\) units is the correct answer.
Learn more about the distance formula here: brainly.com/question/24509115
#SPJ1
Which two complex numbers when added together and written in standard form equal 10-3i?
Answers
Answer:
A -3 − 4i C 13 + i
Step-by-step explanation:
We add the real part and the imaginary part separately.
Adding A and C will give us 10 - 3i:
-3 - 4i + 13 + i
= -3 + 13 - 4i + i
= 10 - 3i.
1. Solve the equation using the zero-product property.
-x(5x – 4) = 0
Answers
Answer:
x = 0, 4/5
Step-by-step explanation:
The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero
Here our a term is -x and our b term is (5x - 4)Setting each term equal to zero and solving for x we get-x = 0 → x = 05x - 4 = 0 → 5x = 4 → x = 4/5find the maximum value of the function f(x)=-1.8x^2+7x-11 to the nearest hundredth.
Answers
The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is, - 4.19.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ f (x) = -1.8x² + 7x - 11
Now, We can differentiate with respect to x as;
⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0
⇒ f ' (x) = - 3.6x + 7
Put f ' (x) = 0
⇒ - 3.6x + 7 = 0
⇒ 3.6x = 7
⇒ x = 1.94
Now, Again differentiate with respect to x as;
⇒ f ' (x) = - 3.6x + 7
⇒ f '' (x) = - 3.6 × 1 + 0
⇒ f '' (x) = - 3.6 < 0
Hence, Substitute x = 1.94 in function to get maximum value,
⇒ f (x) = -1.8x² + 7x - 11
⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11
⇒f (x) = - 6.77 + 13.58 - 11
⇒ f (x) = - 4.19
Thus, The maximum value = - 4.19
Learn more about the function visit:
https://brainly.com/question/28793267
#SPJ1
A deck Corredor is setting up for a reception she purchases 10 containers of flowers with and flowers in each container she divides the total number flowers evenly among the centerpieces if there are twotea centerpieces which expression represents the number of flowers that each centerpiece will contain
Answers
Answer:
The answer is D my friend 10n-t. Hope this Helps :)
Step-by-step explanation:
PLEASE HELP ME PLEASE LOOK AT THE PICTURE BELOW
Answers
Answer:
162 square units
Step-by-step explanation:
You want the surface area of the trapezoidal prism.
Base areaThe triangle at the top of each base is a right triangle with leg 3 units and hypotenuse 5 units. This tells you it is a 3-4-5 right triangle and the width of the prism is 4 units.
The area of each trapezoidal base is ...
A = 1/2(b1 +b2)h = 1/2(3 +6)(4) = 18 . . . . . square units
Lateral areaThe lateral area is the product of the height of the prism (7) and the perimeter of the base. The vertical edges of the base are 3 and 6, the horizontal edge is 4 (see above), and the slant edge is shown as 5. This means the perimeter is 3+6+4+5 = 18 units.
The lateral area of the prism is ...
LA = Ph = (18)(7) = 126 . . . . . square units
Total surface areaThe total surface area of the prism is the sum of the areas of the two bases and the lateral area:
2(18) +126 = 162 . . . . . . square units
The surface area of the composite solid is 162 square units.
__
Additional comment
If you have forgotten about the 3-4-5 right triangle, you can find the missing side length using the Pythagorean theorem.
a² +b² = c²
3² +b² = 5²
b² = 25 -9 = 16
b = √16 = 4 . . . . . . the missing triangle side is 4 units long
<95141404393>
What is the quotient of -27.375 divided by 7.5
A)–3.65
B)–0.365
C)0.365
D)3.65
Answers
Answer: A. -3.65
Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.
\((+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\\)
Knowing this, we can input it into the calculator and find the answer's sign.
\(-27.375/7.5=-3.65\)
Therefore, the answer is A. -3.65.
I hope this helps! Pls mark brainliest!! :)
Help pleasee i am struggling with this question
Answers
The interquartile range of the data is 29
Given that The heights, in feet, of 12 trees in a park are shown below.8 ,11 ,14 ,16 ,17 ,21 , 21, 24,27 ,31 ,43 , 47 and asked to Use the drop-down menus to explain the data's interquartile range.
Interquartile range is the range from the values of quartile 1 (Q1) and quartile 3 (Q3).
To find the interquartile of given heights, arrange the heights in ascending order and find the median.
(8,11,14,16,17,21) ,(21,24,27,31,43,47)
(Q1)quartile 1 =14 ;(Q3)quartile 3 =43.
Interquartile range= quartile 3 - quartile 1
Interquartile range= 43 - 14
Interquartile range=29.
As a result, 29 is the data's interquartile range.
Hence,The interquartile range of the data is 29
Learn more about interquartile here:
https://brainly.com/question/15686744
#SPJ9
Write the equation of y = 1 # when it is shifted 2 units to the left. Then the graph is shifted 7 units upward. Oy= Va + 2 + 7 Oy= ſx - 2+7 Oy = (x + 2) Oy= Vx + 7 + 2
Answers
Answer:
Explanation:
Given:
Equation 1:
\(y=\sqrt[]{x}\)When the first equation is shifted 2 units to the left and 7 units upward, the graph is:
Therefore, the equation for shifting 2 units to the left and 7 units upward is:
\(y=\sqrt[]{x+2}\text{ +7}\)
How could you estimate to get an appointe answer
for this expressions: 12.3 x [(2 x 1.7)] + 6] - 2^3?
Answers
Answer:
Step-by-step explanation:
X = 1 then
(12.3)(1)(2(11.7))+6−23
(12.3)(1)(2(11.7))+6−23
=22.6
Lines a and b are parallel. If the slope of line a is , what is the slope of line b?
A.
-
B.
4
C.
D.
-4
Answers
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines always have the same slope.
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.
what is −5/6÷9/10 HELP FAST
Answers
Answer:
the answer to the question is -25/27
For each ordered pair (x, y), determine whether it is a solution to the inequality y≤0.
(8,-43)
(4.-22)
(-3,25)
(-7,45)
Is it a solution?
Answers
Answer:
(8,-43)
(4,-22)
Step-by-step explanation:
In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.
For example:
(4,-22)
x=4 ; y=-22
Plug y into the inequality
y≤0
-22≤0
Since the statement is true, I know that (4,-22) must be a solution to the inequality.
Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
Answer:
Step-by-step explanation:
To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.
Let's check each ordered pair:
(8, -43):
The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.
(4, -22):
The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.
(-3, 25):
The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.
(-7, 45):
The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.
So, the solutions to the inequality y ≤ 0 are:
(8, -43) and (4, -22).
Petra has 3 packages of ground beef. She has 2 packages weighing 1.11 pounds each and 1 package weighing 1.33 pounds. Petra makes hamburger patties, and each one will be made with exactly 0.25 pounds of ground beef.
To the nearest whole number, what is the greatest number of hamburger patties can she make?
Answers
Answer:
\(\huge\boxed{\sf 14\ patties}\)
Step-by-step explanation:
Total packages = 3
2 packages weighing 1.11 pounds = 2 × 1.11
= 2.22 pounds
1 package = 1.33 pounds
Total weight of packages:
= 2.22 + 1.33
= 3.55 pounds
Each hamburger patty should weigh 0.25 pounds.
Highest number of burgers that can be made:
= Total weight of packages / weight of a hamburger patties
= 3.55 / 0.25
= 14.2 patties
≈ 14 patties
\(\rule[225]{225}{2}\)
The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels
since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005,
the figure was 374 parts per million. Find the increase in carbon dioxide levels and the percent of increase.
Round to the nearest tenth of a percent.
Increase carbon dioxide levels:
Percent increase:
196
Submit Question
parts per million
Question Help: Video Message instructor
Answers
Answer: The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 383 parts per million.
Step-by-step explanation:
;-; my last math question can someone please help meh!
Answers
Answer:
B- Every 3 gallon of red paint requires 1 gallons of yellow paint.
Step-by-step explanation:
I'm not 100% sure on this one. But, it seems like the correct one.
I hope this helps you out!!
What happens at equilibrium price and quanity? 1.The quantity supplied equals the quantity demanded.
2.The price demanded equals the price supplied.
3.The priced demanded equals the quantity supplied.
4.The quantity supplied equals the price demanded.
Answers
Answer:
Step-by-step explanation:
At equilibrium price and quantity, the answer is 1. The quantity supplied equals the quantity demanded.
This means that the market is in a state of balance, where the quantity of a good or service that producers are willing to supply is exactly the same as the quantity that consumers are willing to buy. As a result, there is no excess supply or excess demand, and the price of the good or service is stable.
which location has more vehicles
Answers
Since 2009, the United States is home to the second largest passenger vehicle market of any country in the world, second to China. Overall, there were an estimated 263.6 million registered vehicles in the United States in 2015, most of which were passenger vehicles.