Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution.a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) =b) Find the joint pdf of (X,Y) (f_XY)(x,y)=c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________e) Find the marginal pdf of Y (f_y)( y)= ___________f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________The answer forIs 1/x (0<y<x)Β2x/2 , (x2)/2β , βplease solve e) and f) and g) Beta >0Suppose that that the RV X has the Gamma (2, 3) distribution for some X>0, E(X)=28and V(X) = 2/3². Further, suppose that given X = x, the RV Y has the Unif (0, x)distribution.a)Write down the conditional pdf of Y given X = xSnx (y|x)=b) Find the joint pdf of (X,Y)fx (x, y) =c) Find the conditional mean and variance of YE(Y|X=x)=d)Find the unconditional mean and variance of YV(Y) =E(Y) =e) Find the marginal pdf of Yfy(y) =V(Y|X=x)=Identify the distribution of Y Y-g) Use parts e)- f) to find mean and variance of YE(Y) =V(Y)=

Given that the RV X has the distribution for some , and .Given , the RV Y has the distribution.

Answered: Suppose that that the RV X has the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution.

a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) =
b) Find the joint pdf of (X,Y) (f_XY)(x,y)=
c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________
d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________
e) Find the marginal pdf of Y (f_y)( y)= ___________
f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________

The answer for

Is 1/x (0<y<x)
Β²
x/2 , (x²)/2
β , β

please solve e) and f) and g)

Beta >0
Suppose that that the RV X has the Gamma (2, 3) distribution for some X>0, E(X)=28
and V(X) = 2/3². Further, suppose that given X = x, the RV Y has the Unif (0, x)
distribution.
a)
Write down the conditional pdf of Y given X = x
Snx (y|x)=
b) Find the joint pdf of (X,Y)
fx (x, y) =
c) Find the conditional mean and variance of Y
E(Y|X=x)=
d)
Find the unconditional mean and variance of Y
V(Y) =
E(Y) =
e) Find the marginal pdf of Y
fy(y) =
V(Y|X=x)=
Identify the distribution of Y Y-
g) Use parts e)- f) to find mean and variance of Y
E(Y) =
V(Y)=

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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