8. A pair of jointly continuous random variables, X and Y have the joint density 10 function uniform distributed over 1/2
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- If X is a continuous random variable find the CDF and density of the function y = x/3Let X and Y be two random variables with joint probability mass function: p(x,y) = 1/48 xy(1+y) ??? x=1,2,3 ??? y=1,2 p(x,y) = 0, Otherwise. Please enter the answer to 2 decimal places. What is the variance if (4-2X)?Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.
- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?