STAT 2507 Lecture Notes - Lecture 5: Unimodality, Random Variable, Binomial Distribution

• School: Carleton University
• Department: Statistics
• Course: STAT 2507
• Professor: Zahra Montazeri

Document Summary

Chapter 5 sometimes you cant write the sample state if the number is too large. 2^10 example: toss a dice twice: sample state, random variable: sum of two observed numbers, find pmf mn rule = 36 ways. P(x=k) = (n k) p^k (1-p)^n-k = n!/k!(n-k)! P^k q^n-k n = 10, p = 1/2, x = # of success p(x=5) = (10 5) = (1/2)^5 (1-1/2)^5 p(x<=1) = p(x=0)+p(x=1) = (10 0)(1/2)^0 (1/2)^10 + (10 1)(1/2)^1 (1/2)^9. = 1. 5 + 1. 16 = 2. 66 new - stnd dev = 1. 5 - 1. 16 = 0. 34 p(0. 345) = p(x<=5) = 1-0. 943 p(5