Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,..... 1) for what value of a is the above model meaningful? 2) Verify that the above does represent a legitimate probability distribution. 3) obtain cumulative distribution function of X.

Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,..... 1) for what value of a is the above model meaningful? 2) Verify that the above does represent a legitimate probability distribution. 3) obtain cumulative distribution function of 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

Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,.....

1) for what value of a is the above model meaningful?

2) Verify that the above does represent a legitimate probability distribution.

3) obtain cumulative distribution function of X.

4) show that for any two positive Integers s and t, P(X > s + t | X > s )= P X is great than equal to t).

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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