a. Find k. b. Find P(X<1/4, Y>1/2, 1
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- 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 independentFind a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) = kx; [0, 3]
- Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y 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]Calculate the E(X) when the joint probability density function of X and Y is fxy(X,Y)=c(X+Y) over the range x = 1, ..., 4 and y = 1, ..., 2
- Can you provide a detailed explanation on solving the following problem? Let X and Y have joint probability density funtion :f(x, y) = x + y , for 0 < x < 1 and 0 < y < 1. Are X and Y independent?Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx2; [-1, 2]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).
