Suppose the random variables x,y, and z have joint distribution as follows xy^2z /180 , x-1, 2, 3; У-1, 2; z-1, 2, 3
Find the marginal distribution fi.3(2,3) (round off to third decimal place) of x and z.
Answers
The marginal distribution f(x,3)(2,3) of the random variables x and z
is approximately 0.167.
we first need to compute the marginal distribution f(x,z) by summing over all possible values of y. The given joint distribution function is
\( f(x,y,z) = xy^2z / 180.\)
To compute f(x,z), we sum over all possible values of y:
\(f(x,z) = Σ [f(x,y,z)]\) for all values of y.
For the given values of x = 2 and z = 3:
\(f(2,3) = Σ [f(2,y,3)]\) for y = 1, 2.
\(f(2,3) = f(2,1,3) + f(2,2,3).\)
Now, we'll compute the joint distribution values:
\(f(2,1,3) = (2 * 1^2 * 3) / 180 = 6 / 180.\)
\(f(2,2,3) = (2 * 2^2 * 3) / 180 = 24 / 180.\)
Then, sum the values:
\(f(2,3) = (6 / 180) + (24 / 180) = 30 / 180.\)
Now, we'll round off to the third decimal place:
\(f(2,3) ≈ 0.167\) (rounded to three decimal places).
So, the marginal distribution f(x,3)(2,3) of x and z is approximately 0.167.
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Related Questions
what must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor's degree? why?
Answers
Probability: P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults).
The probability that a randomly chosen young adult has some education beyond high school but not a bachelor's degree would be:
P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults)
where "number of young adults with education beyond high school but not a bachelor's degree" refers to the count of individuals in the population who meet this criteria, and "total number of young adults" refers to the count of all individuals in the population who are considered young adults.
The formula calculates the probability of a certain event by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event is a randomly chosen young adult having some education beyond high school but not a bachelor's degree. The numerator, "number of young adults with education beyond high school but not a bachelor's degree," represents the favorable outcomes, while the denominator, "total number of young adults," represents all possible outcomes.
By dividing the favorable outcomes by the total number of possible outcomes, we get the probability of the event occurring, which is a value between 0 and 1. The closer the value is to 1, the higher the probability that the event will occur. The closer the value is to 0, the lower the probability that the event will occur. This formula allows us to quantify the likelihood of an event occurring in a population based on the available data.
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The second of two numbers is 9 more than 4 times the first. Their sum is 89. Find the smaller number.
HELP ASAP WILL GIVE BRAINLIEST
Answers
Answer:
i think the first number is 20 and the second is 69
Step-by-step explanation:
Answer:
I think the answer is 53
Step-by-step explanation:
9x4=36
And ask what would give you 89 from 36
89-36=53
5.Find the coordinates of the midpoint of the segment
Answers
Answer:
Midpoint formula: (x1+x2/2, y1+y2/2)
Step-by-step explanation:
Take your x points and place them into the formula and then take your y points and do the same.
Answer:
(first)x+(second)x/2(fraction), (first)y+(second)y/2(fraction
Step-by-step explanation:
If you add the x values together and the y values together and divide them both by two you will get your x value for the midpoint and then your y value for the midpoint
Data were collected on the distance a frisbee will travel when thrown at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The regression line is given by y hat equals 3.25 plus 46.89 times s. What are the slope and y-intercept of the regression line and their interpretation in the context of the problem? The slope, 3.25, indicates that the distance decreases by an average of 3.25 yards for every one mile per hour of speed. The y-intercept, 46.89, is the distance estimated by this model if the speed is one mile per hour. The slope, 46.89, indicates that the distance decreases by an average of 46.89 yards for every one mile per hour of speed. The y-intercept, 3.25, is the distance estimated by this model if the speed is one mile per hour. The slope, 3.25, indicates that the distance increases by an average of 3.25 yards for every one mile per hour of speed. The y-intercept, 46.89, is the distance estimated by this model if the speed is zero miles per hour. The slope, 46.89, indicates that the distance increases by an average of 46.89 yards for every one mile per hour of speed. The y-intercept, 3.25, is the distance estimated by this model if the speed is zero miles per hour.
Answers
The gradient m is 4.46 with 3.25 as the intercept
Given,
The regression line is described by the expression
y = 3.25 + 46.89s
Additionally, we can compare the values by writing the expression for the equation of a straight line.
The expression for a straight line is given as
y = mx + c
Where.
m = slope
c = intercept
We may observe that the gradient m = 4.46 by comparing the preceding equation to the straight-line equation.
with a 3.25 as the intercept
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Which of the following sets of numbers could represent the three sides of a triangle? {6,8,14} {13,20,34} {11,14,22} {13,20,35}
Answers
The set of numbers {6, 8, 14} and the set {11, 14, 22} could represent the three sides of a triangle.
To determine whether a set of numbers could represent the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.
Let's evaluate each set of numbers:
1. {6, 8, 14}
The sum of the two smaller sides is 6 + 8 = 14, which is greater than the third side 14. Therefore, this set could represent the sides of a triangle.
2. {13, 20, 34}
The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 34. Hence, this set cannot represent the sides of a triangle.
3. {11, 14, 22}
The sum of the two smaller sides is 11 + 14 = 25, which is greater than the third side 22. Therefore, this set could represent the sides of a triangle.
4. {13, 20, 35}
The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 35. Hence, this set cannot represent the sides of a triangle.
In summary, the sets {6, 8, 14} and {11, 14, 22} could represent the three sides of a triangle.
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Okay so i'm confused about this question. Write an inequality for the phrase ''two more than three times a number is at most 53.''. I don't know witch sign to use!
Answers
Answer:
3m +2≤ 53
Step-by-step explanation:
thats just how it goes logically
please help meeee
will give brainliest
Answers
Answer:
take the number she bought and put it over the amount there are being sold and is the chance of her WINNING and subtract that from 100 and there u go.
Step-by-step explanation:
^
Which figure must have four right angles?
Answers
Answer:
Rectangle
Step-by-step explanation:
Plz Mark Brainliest Thanks
Find the indicated term of the arithmetic sequence with the given description.
The 100th term is - 1240, and the common difference is -25. Find the fifth term.
as = ?
Answers
The fifth term of the arithmetic sequence is -1190.
How to find the arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1) * d
where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.
Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.
Since the fifth term corresponds to n = 5, we can calculate:
a₅ = -1240 + (5 - 1) * (-25)
= -1240 + 4 * (-25)
= -1240 - 100
= -1340
Therefore, the fifth term of the arithmetic sequence is -1190.
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An artist wants to create a painting on a semicircle canvas with a radius of 13 feet. He wants to surround the canvas with a piece of string. The string costs $1. 05 per foot. How much will the piece of string that he needs cost? Round your answer to the nearest dollar
Answers
The artist will need a piece of string that is approximately 40 feet long. Therefore, the cost of the string will be approximately $42.
To calculate the length of the string needed to surround the semicircle canvas, we need to find the circumference of the semicircle. The formula for the circumference of a circle is C = 2πr, where r is the radius. However, since we only need the half-circle, we divide the circumference by 2.
C = (2π * 13) / 2 = 13π ≈ 40.84 feet
Rounding to the nearest foot, the artist needs a string that is approximately 41 feet long. Given the cost of $1.05 per foot, the total cost will be approximately $42.
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Juanita is making a ribbon as shown 4 cm 15 cm 3 cm explain two different ways you can find the area of the ribbon then find the area of the ribbon
Answers
Answer:
6
Step-by-step explanation:
A=hbb/2=4·3/2=6
To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formula
or
The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm2, inches2, and so on.
find the value of x ( 94 , 45, & x)
Answers
Explanation
We are given a triangle
and then asked to determine the value of x
To do so, we know that the total angles in a triangle are 180 degrees
Thus
\(\begin{gathered} x+94+45=180 \\ \\ x+139=180 \\ x=180-139 \\ x=41^0 \\ \end{gathered}\)The value of x is 41 degrees
Help me please I need to finish
Answers
A’ = [ -3 + 6 , 4, 4 ]
B’ = [ 0 + 6 , 1, 4 ]
C’ = [ -4 + 6 , 1, -4 ]
Solution:
A’ = ( 3, 0 )
B’ = ( 6, -3 )
C’ = ( 2, -3 )
can you use the multiplication property of inequality to solve 8m>-1/10?can you use the division of property to solve -9/2 >3/2?explain your reasoning
Answers
a) Yes, by multiplying both sides by 1/8.
b) The inequality is false, thus, there is nothing to solve.
can you use the multiplication property of inequality to solve 8m>-1/10?Yes, you can.
There is a property that says that if you perform the same operation (multiplicating by 1/8 in this case) in both sides, then the truth value of the inequality does not change.
8m > -1/10
So, if we multiply both sides by 1/8, we will get:
8m/m > -1/(10*8)
m > -1/80
The inequality is solved.
can you use the division of property to solve -9/2 >3/2?There is nothing to really solve here, as you can see, the inequality says that a negative number is larger than a positive number, so the inequality is clearly false, and thus, there is nothing to solve.
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What is the name of the ray that is opposite op?
Answers
\( \large \mathfrak{Answer : }\)
The ray opposite to OP is :
OMFind the mean and the standard deviation of the data set {2, 3, 6, 7, 6}.
A. The mean is 4.8 and the standard deviation is about 3.76.
B. The mean is 24 and the standard deviation is about 4.16.
C. The mean is 4.8 and the standard deviation is about 1.94.
D. The mean is 5.2 and the standard deviation is about 2.04.
Answers
Answer: the mean of the data set is 4.8, and the standard deviation is about 1.94. The answer is C.
Step-by-step explanation:
To find the mean and the standard deviation of the data set {2, 3, 6, 7, 6}, we can use the following formulas:
Mean = (sum of all data values) / (number of data values)
Standard deviation = sqrt[(sum of squared differences from the mean) / (number of data values)]
First, we need to find the mean:
Mean = (2 + 3 + 6 + 7 + 6) / 5
Mean = 4.8
Next, we can find the standard deviation:
Calculate the differences between each data value and the mean:
2 - 4.8 = -2.8
3 - 4.8 = -1.8
6 - 4.8 = 1.2
7 - 4.8 = 2.2
6 - 4.8 = 1.2
Square each difference:
(-2.8)^2 = 7.84
(-1.8)^2 = 3.24
(1.2)^2 = 1.44
(2.2)^2 = 4.84
(1.2)^2 = 1.44
Find the sum of the squared differences:
7.84 + 3.24 + 1.44 + 4.84 + 1.44 = 18.80
Divide the sum by the number of data values:
18.80 / 5 = 3.76
Take the square root:
sqrt(3.76) = 1.94 (rounded to two decimal places)
Therefore, the mean of the data set is 4.8, and the standard deviation is about 1.94. The answer is C.
if+the+correlation+between+two+variables+is+.496,+how+much+of+the+variance+has+not+been+accounted+for?++a.+24.6%++b.+49.6%++c.+50.4%++d.+75.4%
Answers
The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.
If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.
A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.
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Add. 3/7 + 6/7 pls helppppppppppppppppppppp
Answers
Answer:
9/7
or
1 2/7
Step-by-step explanation:
use math-way it
3/7+6/7=9/7
3/7+6/7=3+6/7=9/7
Which is equivalent to 4√3
will mark brainlist if right
Answers
Answer:
The result can be shown in multiple forms.
Exact Form: 4√3 = √48
Step-by-step explanation:
4√3 is equivalent to √48
A store pays $8 for a pool noodle. The markup is 20%. What is the selling price?
Answers
Answers: he markup price is $9.6
You will be paying 120% which is 1.20 as a decimal
So you multiply. 8(1.20) which gives you $9.6
Step-by-step explanation: thank you for letting me answer this question hope it's helpful
if two sides of a triangle are 22 in and 13 in, what is the smallest whole number value for the 3rd side?
Answers
If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
According to the rule of triangle the sum of first angle and second angle should be greater than the third angle.
first angle+ second angle > third angle
Here
22-13 = 9
so to became a triangle the minimum value of the third side will be 10(9+1).
Therefore, If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
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Matthew has a standard deck of cards. There are four suits with 13 cards in each from ace through to king. He shuffles the deck and selects one card and then another. In its simplest form, what is the probability that he draws a pair of tens? 1st attempt: probability of getting a pair of 10s.
Answers
The probability that he draws a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%
The probability of drawing a pair of tens from a standard deck of cards is (number of ways to get a pair of tens) / (total number of possible outcomes).
In this case there are 4 tens (2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs) and he is drawing 2 cards from the deck, so there is only 1 way to get a pair of tens. There are 52 cards in a standard deck, so the total number of possible outcomes is 52 * 51 = 2652.
So the probability of drawing a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%
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You went to Walmart and you bought a hoverboard. The total cost was $150.00 which includes a tax of 6%. What was the original price?
Answers
Answer:
$141
Step-by-step explanation:
150x.06=9
150-9=141
not sure this is right, its off the top of my head and it's been a while since I've been in a math class that does this so i apologize in advance
classify the following triangle check all that apply
A.Isosceles
B.Scalene
C.Right
D.Obtuse
E.Acute
F.Equilateral
Answers
Answer:
c.Right
Step-by-step explanation:
because of the 90 degrees it shows that it is 90 degrees
Answer:
B. scalene
C. right
Step-by-step explanation:
Find x, and GH.
X =
GH: =
34
7x + 6
4x + 8
Answers
By using given figure, x=9/4 and the length of GH = 21.75.
What is the length ?
Here, in given figure,
BG≈GF and CH≈HE
now by using these similarities, we can write as,
BG≈GF therfore, \(\frac{GF}{BG}\) = 1:1
\(\frac{GF}{BF}\)=\(\frac{4x+8}{34}\)
1/2=\(\frac{4x+8}{34}\)
8x+16=34
8x= 18
x=9/4
if x=9/4 then,
GH= 7x+6 = 7(9/4)+6 =63/4+6 =\(\frac{63+24}{4}\) = 21.75
What is similarity of sides?
similarity of sides refers to the property of two geometric shapes or figures having the same shape but not necessarily the same size. More specifically, two shapes are said to be similar if their corresponding angles are congruent and their corresponding sides are proportional in length.
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students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.
Answers
we know that
The formula for combinations is
\(C=n!/[(n-r)!*r!]\)
where
\(n\) is the total number of objects you choose from
\(r\) is the number that you choose to arrange
in this problem
\(n=15\) students
\(r=4\) students
\(C=15!/[(15-4)!*4!]\) → \(C=15!/[11!*4!]\) → \((15*14*13*12*11!)/(11!*4*3*2*1)\)
\(C=(15*14*13*12)/(24)\) → \(C=1365\)
the answer is
1,365
Let A = PDP-1 and P and D as shown below. Compute A4. P 1 3 3 0 P= D 2 5 0 1 시 A4 = (Simplify your answer.) -1 Use the factorization A = PDP to compute Ak, where k represents an arbitrary integer. a 9(b-a) 1 9 a 0 1 -9 = 0 b 0 1 ob 0 1 AK =
Answers
the average value of f(x) = 5x^2 over the interval [1,4] is 315/9, which can be simplified to 35/1 or simply 35.
To determine the average value of the function f(x) = 5x^2 over the interval [1,4], we need to calculate the definite integral of the function over the given interval and divide it by the length of the interval.
The average value of a function f(x) over the interval [a, b] is given by the formula:
(1 / (b - a)) * ∫[a to b] f(x) dx
In this case, we have f(x) = 5x^2 and the interval is [1,4]. Therefore, the average value of f(x) over the interval [1,4] is:
(1 / (4 - 1)) * ∫[1 to 4] 5x^2 dx
Evaluating the definite integral, we get:
(1 / 3) * [ (5/3)x^3 ] evaluated from x = 1 to x = 4
Substituting the limits into the expression, we have:
(1 / 3) * ( (5/3)(4^3) - (5/3)(1^3) )
Simplifying further, we get:
(1 / 3) * ( (5/3)(64) - (5/3)(1) )
= (1 / 3) * ( (320/3) - (5/3) )
= (1 / 3) * ( (320 - 5) / 3 )
= (1 / 3) * ( 315 / 3 )
= 315 / 9
Therefore, the average value of f(x) = 5x^2 over the interval [1,4] is 315/9, which can be simplified to 35/1 or simply 35.
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due today help meeeeeee
Answers
Answer:
√(209)
Step-by-step explanation:
Since <B is a right angle, AC is the hypotenuse and AB and BC are legs.
(AB)² + (BC)² = (AC)²
(4 mm)² + (BC)² = (15 mm)²
16 mm² + (BC)² = 225 mm²
(BC)² = 209 mm²
BC = √(209) mm
Pls help will mark the brainiest
Answers
Answer:
Negative
Step-by-step explanation:
Since the value of A is larger than B, and A is negative, we go with the sign of A which ends up being negative.
Have a nice day!
If this is not what you are looking for - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
negative
Step-by-step explanation:
Angles that measure 135 degrees and 45 degrees are complementary,
True or false?
Answers
Answer:
FAlse
complementary angles measures 90
as 45 + 135 = 180 these are supplementary angles
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Complementary angles are when either of two angles whose sum is 90°.