Class VIdeo 11 Notes - Binomial Distribution | McMaster University - Edubirdie

University:
McMaster University
Course:
STATS 1LL3 | Introduction to Probability and Statistics
Academic year:

2023
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145

Pages:

2
Author:

Sabrina S.

Video 11: Binomial Distribution Example: Teaching mice to read. Set off in a maze, sign says turn left. 4 of the 5 mice turn left. Question: Does the mouse turn left or right? Answer: Random outcome. If mice cannot read: Event of Interest: Probability of 4 out of 5 mice turning left? Random Variable: The number of mice that turn left out of 5 potential mice. Y: The number of mice that successfully negotiate the maze. P: Probability of each mouse turning left (success). Possible outcomes: No mice, one mouse, ..., five mice. Probability: For each possible outcome, calculate the associated probability. Formula: P(x=x) = (n choose x) * p^x * (1-p)^(n-x) for x = 0, 1, 2, ..., n and 0 elsewhere. The probability of 4 mice turning left by chance when they can't read visual clues is given by: Pr(x=4) = (5 choose 4) * 0.5^4 * (1-0.5)^1 = 0.156 Binomial Distribution Random variable: records the number of successes in n trials of an experiment with probability p of success. which remains constant on each trial P(x=x) = (n choose x) * p^x * (1-p)^(n-x) for x = 0, 1, 2, ..., n and 0 elsewhere. ... binomial distribution: X ~ B(n, p)

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