3. (12 points) The continuous random variable X has the probability density function (PDF) fx(x) =ce for x = 0 and 0 otherwise. 1} (2 points) Find the value of the constant . 2) ( 3) (4 points) Find the expectation E{X) and the variance var{ X). 4) (4 2 points) Find the cumulative distribution function (CDF) of X, namely, Fy(x). points) Find the variance of X2, namely, var(X?). 4. (10 points) The discrete integer-valued random variables X and Y have the joint probability mass function (PMF) xy(T,y) =P(X =2,Y =y) =c(z +y)* for x {-2.2}, y {1,1} and 0 otherwise. 1} (2 points) Find the value of the constant . 2) 3) ) 5) 2 points) Find the expectation E{X) and the variance var(X). 4 ( ( ) (2 points) Find the expectation E(Y) and the variance var(Y). (2 points) Find the conditional probability P(Y = 1| X = -2). ( ) 2 points) Are X and Y independent? Explain why