Probability

You may review the concepts about Randomization and Probability from the Textbook. You may learn the detailed introduction to concepts Expected Value and Linearity of expectation from this MIT lecture video.

Self-Testing Quizzes

1. The expectation of a random variable X(continuous or discrete) is given by _________

\( ∑xf(x), ∫xf(x) \) \( ∑x^2 f(x), ∫x^2 f(x) \) \( ∑f(x), ∫f(x) \) \( ∑xf(x^2), ∫xf(x^2) \)

2. Mean of a random variable X is given by _________

\( E(X) \) \(E(X^2) \) \( E(X^2) – (E(X))^2 \) \( (E(X))^2 \)

3. Find the mean and variance of \(X\)?

\(x\)	0	1	2	3	4
\(f(x) \)	1/9	2/9	3/9	2/9	1/9

0 1 2 5

4. Let there be a group of \(n \) men where every man has one hat. The hats are redistributed and every man gets a random hat back. What is the expected number of men that get their original hat back?

\( n \) 1 \( {1}\over {n} \) 0