HW#3, Due 03/07
AMS 311 Probability Theory (Spring 2011)
Read: Ross, Chapter 4, Sections 4.1–4.5. You may skip Example 1e, Example 4c
Part 1 (10 points):
PRINT
your name and StonyBrook ID (
Last, First, #ID
) on the top on your work
sheet. Staple your HW if more than 1 pages.
Part 2: Problems (90 points)
Write down your work step by step to get full score.
(1). (20 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). (9 points) Give (explicitly) the probability mass function for X. Also show a plot
of it.
(b). (7 points) Give (explicitly) the cdf, F(x), for X. Also show a plot of it.
(c). (4 points) 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
(a). (4 points) Give the probability mass function, p(x), of X, explicitly.
(b). (3 points) Compute P(2 < X < 3).
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 Spring '08
 Tucker,A
 chem ist ry, ist ry majors

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