Consider n independent trials of a \"success-failure\" experiment (with probability of success being p). Let X be the random variable that denotes the total number of \"successes\" in 11 trials. (a) ( 2 pt) What are the values that the random variable X takes? (b) (2 pt) Write down the expression which calculates the probability for X = k \"successes\" : P(X = k) (c) ( 6 pt) We also proved that E (X) = np [ Problem 64, section 3.4) Show that Var(X) = up (1 - p)