Calculate the PMF of X. 2. Find the expectation and the variance of X. 3. Suppose Tharun has to pay $3 to enter the shooting range and he gets $2 dollars for each hit. Let Y be his profit. Find the expectation and the variance of Y .

Calculate the PMF of X. 2. Find the expectation and the variance of X. 3. Suppose Tharun has to pay $3 to enter the shooting range and he gets $2 dollars for each hit. Let Y be his profit. Find the expectation and the variance of Y .

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

Tharun being poor at shooting takes 10 shots at a target and has probability 0.2
of hitting the target with each shot, independently of all other shots. Let X be the
number of hits.
1. Calculate the PMF of X.
2. Find the expectation and the variance of X.
3. Suppose Tharun has to pay $3 to enter the shooting range and he gets $2 dollars
for each hit. Let Y be his profit. Find the expectation and the variance of Y .
4. Now let’s assume that Tharun enters the shooting range for free and gets the
number of dollars that is equal to the square of the number of hits. Let Z be his
profit. Find the expectation of Z.

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