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- Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwiseQ3) The joint probability density function of two discrete random variables X and ¥ is given by p(x, y)=c(2x+3y), where x and can assume all integers such that 0 <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).
- Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.Find the joint probability density of the two randomvariables X and Y whose joint distribution function isgiven byF(x, y) = (1 − e−x2)(1 − e−y2) for x > 0, y > 00 elsewhereFind a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx3; [2, 4]