Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by p(x) = (cx for x = 1, 2, 3, 4, 5, 6 0 otherwise) (a) Find the value of c that makes p(x) a valid PMF. (b) Compute E[X]. (c) Compute E[X^2]. (d) Compute the standard deviation of X, SD(X). (e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate P(E[X] − SD(X) < X < E[X] + SD(X)).

Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by p(x) = (cx for x = 1, 2, 3, 4, 5, 6 0 otherwise) (a) Find the value of c that makes p(x) a valid PMF. (b) Compute E[X]. (c) Compute E[X^2]. (d) Compute the standard deviation of X, SD(X). (e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate P(E[X] − SD(X) < X < E[X] + SD(X)).

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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Question

Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by
p(x) = (cx for x = 1, 2, 3, 4, 5, 6
0 otherwise)
(a) Find the value of c that makes p(x) a valid PMF.
(b) Compute E[X].
(c) Compute E[X^2].
(d) Compute the standard deviation of X, SD(X).
(e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate
P(E[X] − SD(X) < X < E[X] + SD(X)).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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