Expected Value and Variance

STAT 20: Introduction to Probability and Statistics

Agenda

• Concept review
• Concept questions
• PS 10
• Break
• Lab 3 slides
• Lab 3

Concept Review

Let $X$ be a random variable such that $X = \begin{cases} -1, & \text{ with probability } 1/3\\ 0, & \text{ with probability } 1/6\\ 1, & \text{ with probability } 4/15 \\ 2, & \text{ with probability } 7/30 \\ \end{cases}$

1. Draw the graph of the cdf of $X$
08:00

1. Compute the expected value and variance of $X$

Concept Questions

01:00

$X$ is a random variable with the distribution shown below:

$X = \begin{cases} 3, \; \text{ with prob } 1/3\\ 4, \; \text{ with prob } 1/4\\ 5, \; \text{ with prob } 5/12 \end{cases}$

Consider the box with tickets: $\fbox{3}\, \fbox{3}\, \fbox{3} \,\fbox{4} \,\fbox{4} \,\fbox{4} \,\fbox{4} \,\fbox{5} \,\fbox{5}\, \fbox{5} \,\fbox{5} \,\fbox{5}$

Suppose we draw once from this box and let $Y$ be the value of the ticket drawn. Which random variable has a higher expectation?

The expected value of $X$ is ____ the expected value of $Y$.

01:00

Prof. Stoyanov’s Zoom office hours are not too crowded this spring. She observes that number of Stat 20 students coming to her Thursday office hours have a Poisson(2) distribution. There is one Data 88 student from a previous semester who is always there (they want a letter of recommendation).

What is the expected value (EV) and variance (V) of the number of students in her Zoom office hours?

01:00

Let $X$ be a discrete uniform random variable on the set $\{-1, 0, 1\}$.

If $Y=X^2$, what is $E(Y)$?

01:00

Let $X$ be a discrete uniform random variable on the set $\{-1, 0, 1\}$.

If $W = \min(X, 0.5)$, what is $E(W)$?

PS 10

25:00

Break

05:00