# Random Variables

STAT 20: Introduction to Probability and Statistics

## Agenda

• Brief lecture on probability distributions and random variables
• Review quiz 3
• Concept questions
• Break
• Handout: PS 4.1 (random variables)

# Concept Questions

01:00

Is the following random variable binomial (if so, what are $n$ and $p$?), hypergeometric (if so , what are $N$, $G$, and $n$?), or neither?

Roll a fair ten-sided die 20 times. Let $X$ be the number of times we roll a multiple of 3.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are $n$ and $p$?), hypergeometric (if so , what are $N$, $G$, and $n$?), or neither?

Poll 1,000 Chicago residents and ask them if they voted for Lori Lightfoot in the mayoral election. Let $X$ be the number of people who respond “Yes”. The population of Chicago is about 2.7 million.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are $n$ and $p$?), hypergeometric (if so , what are $N$, $G$, and $n$?), or neither?

A six-sided die is tossed two times and the sum of the faces showing is $8$. Let $X$ be 1 if the sum is $8$ and $0$ otherwise.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are $n$ and $p$?), hypergeometric (if so , what are $N$, $G$, and $n$?), or neither?

A bag that has 6 pieces of fruit: 2 mangoes, 3 apples, and 1 orange. I reach into the bag and draw out one fruit at a time, selecting each fruit at random (so they are equally likely). Let $X$ be the number of draws until and including the first time I draw a apple.

Binomial, hypergeometric, or neither?

01:00

You have $10$ people with a cold and you have a remedy with a $20\%$ chance of success. What is the chance that your remedy will cure at least one sufferer? (Let $X$ be the number of people cured among the 10. We are looking for the probability that $X \ge 1$)

What is the chance that at least one person is cured?

03:00

Roll a pair of fair six-sided dice and let $X = 1$ if the dice land showing the same number of spots, and $0$ otherwise. For example, if both dice land $2$, then $X = 1$, but if one lands $2$ and the other lands $3$, then $X = 0$.

What is $P(X=1)$?

# Break

05:00