Page 3 (06 (25 points) Answer the following questions by using the following Probability Distribution Table: (Random Variable X represents the number of phone calls in a family during last weekend). (a) Use the table and find the probabilities of the following cases: (i ) P(X = 2) = ANS. (ii) P(at least X = 2) = ANS. (iii) P(at most X = 2) = ANS. (iv) P(X = 2 OR X=3) ANS. (iv) P(X =2 AND X=3) ANS. (b) Find the mean, variance and standard deviation of the random variable X. ANS. mean: ANS. Variance: ANS. Standards deviation: X P(X) 0 0.12 0.41 2 0.31 3 0.10 4 0.06