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In: Statistics and Probability

f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta...

f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1.

a). show that f(y) the marginal density function of Y is a Beta random variable with parameters alfa=3 and Beta=3.

b). show that f(x|y) the conditional density function of X given Y=y is a Gamma random variable with parameters alfa=2 and beta=y.

c). set up how would you find P(1<X<3|Y=.5). you do not have to do any calculations

Solutions

Expert Solution

Answer a:

Y is a Beta Random variable with parameters alpha=3 and Beta=3

Answer b:

Conditional Density function of X given Y=y, follows gamma distribution with alpha=3 and beta=y

Answer c:

The value of the integrand to be calculated is shown in the answer.

orchestra answered 2 years ago
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