Math 362 - Computer Lab #4 - Fall 2002
Introduction
to Probability Theory
Computer Lab 4: More on Random Variables
Solve the word problems below and use the computer to check your answers either
by simulation and/or with the Calc -> Probability Distributions
function.
- (From A First Course in Probability by
Sheldon Ross, Prentice Hall, 2002)
Two balls are chosen randomly from an urn containing 8 white, 4 black and 2
orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for
each white ball selected. Let X denote our winnings. What are the possible values
of X and what are the probabilities associated with each value?
- (From A First Course in Probability by
Sheldon Ross, Prentice Hall, 2002)
Two fair dice are rolled. Let X equal the product of the 2 dice. Compute
Pr (X = i) for i = 1, 2, ...
- (From A First Course in Probability by
Sheldon Ross, Prentice Hall, 2002)
Let X represent the difference between the number of heads and the number
of tails when a coin is tossed 3 times. What are the possible values of X and
what are the corresponding probabilities?
- (From An Introduction to Mathematical Statistics and its Applications by
R.J. Larsen & M.L. Marx, Prentice Hall, 2001) An urn contains five chips, numbered 1 through 5.
Two are drawn without replacement. Tabulate the p.m.f. for X, the larger of the two.
- (From An Introduction to Mathematical Statistics and its Applications by
R.J. Larsen & M.L. Marx, Prentice Hall, 2001) An urn contains four chips, numbered 1 through
4, where the probability associated with a chip is proportional to its magnitude. Find and
graph the c.d.f. corresponding to the number showing on the chip drawn at random.
The macro Loop.MTB illustrates how the results of a simulation
(here the sampling without replacement of 2 numbers from Column C1) may be stored in a
single column (here C3) when an exec is run more than once. You may try and modify this file
at your convenience.
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