Random Variables by David Spade, PhD

About the Lecture

The lecture Random Variables by David Spade, PhD is from the course Statistics Part 1. It contains the following chapters:

Random Variables
Expected Values
Evaluating Spread
Properties of Variances

Included Quiz Questions

What best describes a numeric value based on the outcome of a random event?

A numeric value based on the outcome of a random event is known as a random variable.
A numeric value based on the outcome of a random event is known as a probability model.
A numeric value based on the outcome of a random event is known as an expected value.
A numeric value based on the outcome of a random event is known as a random phenomenon.
A numeric value based on the outcome of a random event is known as a unique variable.

In a coin-flipping game, you get two points for heads, and you lose one point for tails. The coin is heads with probability of 1/3 and tails with probability of 2/3. What is the expected value of X that corresponds with the number of points for a coin flip?

The expected value of X is 0.
The expected value of X is 1.
The expected value of X is -1.
The expected value of X is 3.
The expected value of X is 1/3.

In a coin-flipping game, you get two points for heads, and you lose one point for tails. The coin comes up heads with probability 1/3 and tails with probability 2/3. What is the variance, given by the value X?

The variance of X is 2.
The variance of X is -1.
The variance of X is 0.
The variance of X is 5.
The variance is -2.

In a coin-flipping game, you get two points for heads, and you lose one point for tails. The coin comes up heads with probability 1/3 and tails with probability 2/3. You independently flip the coin twice. What are the expected value and the variance for two coin flips?

The expected total is 0 and the variance is 4.
The expected total is 0 and the variance is 0.
The expected total is 1 and the variance is 4.
The expected total is 0 and the variance is 2.
The expected total is 1 and the variance is 2.

Which of the following is TRUE of random variables?

For any two independent random variables X and Y, Var (X+Y) = Var (X) + Var (Y).
For any two random variables X and Y, SD (X+Y) = SD (X) + SD (Y).
For any two independent random variables X and Y, SD (X+Y) = SD (X) + SD (Y).
For any two random variables X and Y, Var (X+Y) = Var (X) + Var (Y).
For any two random variables X and Y, Var (X+Y) = Var (X) * Var (Y).