Answer all the questions

5. Find the standard deviation of the probability distribution in Problem 4. 6. The probabilities that a production process will produce 0, 1, 2, 3, 4 or 5 units in one hour are 0.05, 0.16, 0.21, 0.34, 0.22 and 0.02 respectively. Find the mean and the variance of this probability distribution. 7. Let X represent the outcome when a balanced die is tossed. If g(X) = 3X2+4, Find: a) /(X) b ) 0 8 ( x )8. The probability distribution of the discrete random variable X is: f ( x ) = ( )= ) ( = )3- for x = 0, 1, 2, 3 Find the mean of X. 9. Find the expected value of the random variable g(X) = X where X is the probability distribution of Problem 8.10. Suppose that X and Y have the following joint probability function: 2 4 0.10 0.15 3 0.20 0.30 5 0.10 0.15 Find the expected value of g(X, Y) = XY2