Lecture 16

Faculty of Science; Department of Mathematics
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Readings For This Lecture

Keshet Course Notes:

Chapter 7, pages 150 to 152

Summary

Group 10: Add a summary of the lecture in this space. Include examples, discussion, and links to external sources, if desired.

Exercises

1. The $j^{th}$ moment of a distribution is

$M_{j}=\sum _{i=0}^{N}(x_{i})^{j}p(x_{i})$ .

Show that for a discrete probability distribution, $M_{0}=1$ and $M_{1}$ corresponds to the average value. Also show that the variance can be expressed as

$V=M_{2}-(M_{1})^{2}$ .

2. You are out fishing. Everytime you cast your line, the probability that you catch a fish is \frac{1/4}. What is the probability that you catch at least one fish within the first 2 attempts? | ! Solution | \frac{1/4} + \frac{1/4}= \frac {1/2}

3. A biased coin with P(H)=1/10 is tossed 4 times. What is the probability of getting at least one H? Solution

Use the fact that this is a Bernoulli Trial. So 1-(chance of not getting a head)^4 This equals 1-(9/10)^4