a) What is the marginal distribution of Z2. b) Find P(Z2 <4)
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- Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?
- Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.Suppose that X and Y have a joint probability density function given by: ( only for D) and E), ignored A),B)and C))Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independent
- Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]
