1) Let X the random variable representing the number of cars sold per week with a car-sales company. It has been observed (10 years records) that X can assume the values 0,1,2,3,4 with probabilities py, p1, P2, P3, Ps, respectively. These probabilities are related as shown below: 0o Po = P2 Py = P3 P3 = 2po, Py = %p3 Given that all five probabilities (pg, p1, P2, P3,P4) should add to 1, find the probability mass function of X, i, e. f(x). Compute E(X) and Var(X). Find the cumulative distribution function of , I, e. F (x). Compute the probabilities: P(X2),P(X=2o0r 3), F(1), F(2.2), F(3.99), F(10). Suppose a salesman in the company is paid per week 100 plus 130 for each car he sales. Let V the random variable representing his payment per week. Find E(Y) and the corresponding standard deviation. It is known that: E(Y)=E(aX+p) =aE(X) t B Var(Y) = Var(aX + B) = a? Var(X) (25 points)