a) What is conditional probability? b) Show that var(aX+bY)= a² var (X) + b² var (Y) + 2ab cov (X,Y). c) If X is a continuous random variable, show that variance of X equals E[X²]-Hx² X and Y are continuous random variables where x & [0,1] and y & [0,1]. The joint probability density function of X and Y is f(x,y) = x+y. Calculate the conditional mean of X given that Y=1/4. > Calculate the conditional variance of X given that Y=1/4. State and briefly explain all the assumptions of the Simple Linear Regression Model