# 2/13/2023

## Discussion of Quiz #2.

## The mean (expected value) and standard deviation of
a random variable

- Mean (or Expected Value) of X
- If X is a discrete random variable taking values x
_{1}, x_{2}, …, x_{k} with probabilities p_{1}, p_{2}, …, p_{k} the mean (or expected value) of X is given by µ=E[X] = x_{1}*p_{1} + x_{2}*p_{2} + ... + x_{k}*p_{k}.

- Variance of X
- If X is a discrete random variable taking values x
_{1}, x_{2}, …, x_{k} with probabilities p_{1}, p_{2}, …, p_{k} the variance of X is given by Var[X] = (x_{1}-µ)^{2}*p_{1} + (x_{2}-µ)^{2}*p_{2} + (x_{k}-µ)^{2}*p_{k}.
- The standard deviation of X is the square root of the variance.

## Conditional Probability and Bayes Theorem - (see Section3.2_Conditional_Probability_Bayes_Rule.pdf in our !Class-Notes Google Drive folder.

## Properties of means and variances - (see Section3.4_Means_Variances.pdf)

## Class Activities - See handouts

- Applications of Bayes Theorem
- Means and Variances of Discrete Random Variables

## Please complete your reading of Section 4.1 for class on Wednesday.

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