Homework 3

	Student A
Full Name	Ido Fang Bentov
ID	CLASSIFIED
Email	CLASSIFIED

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Question 1

Which one of the following assertions is correct and which one is false:
1.
E(2{X}{1})=E({X}{1}+{X}_{2})

Solution:

1. Only if , because then
2. Incorrect. Say . Then And:

Question 2

You take an exam that contains multiple-choice questions. Each question has possible options. You know the answer to questions, but you have no idea about the other questions so you choose answers randomly. Your score on the exam is the total number of correct answers. Find the PMF of . What is ?

Solution:
Denoting as the number of randomly guessed answers that are correct, then we get . According to binomial distributions, the PMF of is:

Therefore:

In order to compute we need to compute:

In total, we get: