AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 3 Due at the beginning of class on Thursday, September 24, 2009. Reminder: Show your reasoning! Read: Ross, Chapter 4, Sections 4.1–4.5. You may skip Example 1e, Example 4c (1). (30 points) A box contains 10 dimes, 15 nickels, and 4 pennies. We draw 2 coins at random (without replacement). Let X represent the amount (in cents) that we draw out of the box. (a). Give (explicitly) the probability mass function for X . Also show a plot of it. (b). Give (explicitly) the cdf, F ( x ), for X . Also show a plot of it. (c). How much money do we expect to draw from the box? (2). (25 points) Consider a random variable X whose distribution function (cdf) is given by F X ( x ) = 0 if x <-20 . 1 if-2 ≤ x < 1 . 10 . 3 if 1 . 1 ≤ x < 20 . 6 if 2 ≤ x < 3 1 if x ≥ 3 (a). Give the probability mass function of X , explicitly. (b). Compute
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