Probability

You may review the concepts about Randomization and Probability from the Appendix C of the CLRS textbook on pages 1183-1216. 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