f(x,y)=30(1-y)^2xe^(-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 1 year ago

Next > < Previous

Related Solutions

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation...

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation coefficient ρX,Y . 5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y)...

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y) = 0 otherwise. (a) Indicate with a sketch the sample space in the x-y plane (b) Find the marginal density of X, fX(x) (c) Show that fX(x) is properly normalized, i.e., that it integrates to 1 on the sample space of X (d) Find the marginal density of Y, fY(y) (e) Show that fY(y) is properly normalized, i.e., that it integrates to 1 on...

Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find...

Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find the correlation--ROW p (X,Y) .

For f(x,y)=cxy, ? ≥ 0, ? ≥ 0, ? + ? ≤ 1, Determine E(Y|x) and...

For f(x,y)=cxy, ? ≥ 0, ? ≥ 0, ? + ? ≤ 1, Determine E(Y|x) and E(X|y)

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value of k that makes this a probability density function. Compute the probability that P(X≤3/4, Y≥1/2). Find E(X). Find E(X|Y=y).

Show that this function has a positive maximum on the interval 0<_x_<1: f(x)=x(x-1)e^x

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does not equal to 0 3. f'(0)=1 Then: a) Show that f(0)=1. (Hint: use the fact that 0+0=0) b) Show that f(x) does not equal to 0 for all x. (Hint: use y= -x with conditions (1) and (2) above.) c) Use the definition of the derivative to show that f'(x)=f(x) for all real numbers x d) let g(x) satisfy properties (1)-(3) above and let...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is a joint pdf. b. Find the correlation coefficient of X and Y.

solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0

Subjects

Question

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...

Solutions

Expert Solution

Related Solutions

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