AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 3 Due at the beginning of class on Thursday, September 30, 2010. Reminder: Show your reasoning! Read: Ross, Chapter 4, Sections 4.1–4.5. You may skip Example 1e, Example 4c (1). (30 points) In your pocket, you have 2 dimes, 2 nickels, and 1 penny. You select 3 coins at random (without replacement). Let X represent the amount (in cents) that you select from your pocket. (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 you expect to draw from your pocket? (2). (25 points) Consider a random variable X whose distribution function (cdf) is given by F X ( x ) = 0 if x <-10 . 2 if-1 ≤ x < 1 . 20 . 3 if 1 . 2 ≤ x < 20 . 5 if 2 ≤ x < 30 . 6 if 3 ≤ x < 4 1 if x ≥ 4 (a). (6 points) Give the probability mass function, p ( x ), of X , explicitly. (b). (3 points) Compute
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