Exercise 1 (a) True/False. The mean of a discrete random variable must be a possible value of the random variable. (b) True/False. The expected value of a discrete random variable can be negative. (c) True/False. The standard deviation of a discrete random variable is always nonnegative. (d) Fill in the Blank. The variance of a discrete random variable is the expected value of (e) True/False. The standard deviation of a discrete random variable could be 0. (f) Fill in the Blank. Suppose f(X) is a function of a discrete random variable. E(f(X)) =Exercise 5 A box contains n chips numbered 1 through n. One chip is drawn from the box as follows: the probability of choosing chip i is equal to ki (i = 1,2, ... , n) where k is a constant. Let X denotes the number showing on the chip selected.Exercise 4 A rpical day's production of a certain electronic component is twelve. The probability that one of these components needs rework is {1.1 1. Each component needing rework costs $100. What is the average daily cost for defective components? Exercise 2 A problem in a test given to small children asks them to match each of three pictures of animals to the word identifying that animal. If a child assigns the three words at random to the three pictures, find the probability distribution for Y, the number of correct matches. Exercise 3 The manager of a stockroom in a factory has constructed the following probability distribution for the daily demand (number of times used) for a particular tool. y 0 1 2 p(y) .2 .5 .3 It costs the factory $10 each time the tool is used. Find the mean and variance of the daily cost for use of the tool