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 x1, x2, …, xk with probabilities p1, p2, …, pk the mean (or expected value) of X is given by µ=E[X] = x1*p1 + x2*p2 + ... + xk*pk.
- Variance of X
- If X is a discrete random variable taking values x1, x2, …, xk with probabilities p1, p2, …, pk the variance of X is given by Var[X] = (x1-µ)2*p1 + (x2-µ)2*p2 + (xk-µ)2*pk.
- 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.