Lecture 15

Faculty of Science; Department of Mathematics
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Readings For This Lecture

Keshet Course Notes:

Chapter 7, pages 146 to 150 (up to subsection 7.8)

Summary

Group 9: Add a summary of the lecture in this space. Include examples, discussion, and links to external sources, if desired.

Exercises

1. Determine the probabilities of getting 1, 2, 3, or any number k ≤ 8 of Heads when a fair coin is tossed 8 times. Give your results in the form of a table.

Prob(1)=(8/1)*(1/2)^(1)*(1/2)^(8-1) = (8/1)*(1/2)*(1/2)^(7) Prob(2)=(8/2)*(1/2)^(2)*(1/2)^(6) Prob(3)=(8/3)*(1/2)^(3)*(1/2)^(5) prob(4)=(8/4)*(1/2)^(4)*(1/2)^(4) Prob(5)=(8/5)*(1/2)^(5)*(1/2)^(3) Prob(6)=(8/6)*(1/2)^(6)*(1/2)^(2) Prob(7)=(8/7)*(1/2)^(7)*(1/2)^(1) Prob(8)=(8/8)*(1/2)^(8)*(1/2)^(0)

2. Suppose the coin in question 1 is not fair, so that the probability of heads is $p=0.45$ . Determine the probability of getting exactly 3 heads in a total of 8 tosses.

Using Bernoulli trials = (N/K)*P^(K)*Q(N-K) =(8/3)*(0.45)^(3)*(0.55)^(5)

3. Give a table for the cumulative distribution corresponding to the 8 coin toss experiment for a fair coin.