Roll a fair die 60 times. Let X be the number of sixes. (a) Find the Probability Mass Function (PMF) of X (remember to define the scope of x) (b) Find the probability that X is odd (c) Find the Cumulative Density Function of X (remember to define the scope)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Roll a fair die 60 times. Let X be the number of sixes.
(a) Find the Probability Mass Function (PMF) of X (remember to define the
scope of x)
(b) Find the probability that X is odd
(c) Find the Cumulative Density Function of X (remember to define the scope)
(d) Find the probability that X is greater than or equal to 4. (Hint: P(X > 4))
(e) Find the expected value of X, and briefly explain what this number
represents
(f) Find the variance of X, and briefly explain what this number represents?
Transcribed Image Text:Roll a fair die 60 times. Let X be the number of sixes. (a) Find the Probability Mass Function (PMF) of X (remember to define the scope of x) (b) Find the probability that X is odd (c) Find the Cumulative Density Function of X (remember to define the scope) (d) Find the probability that X is greater than or equal to 4. (Hint: P(X > 4)) (e) Find the expected value of X, and briefly explain what this number represents (f) Find the variance of X, and briefly explain what this number represents?
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