4. Probability, Random Variables, and Probability Distributions

Transforming Random Variables — Quiz

Test your understanding of transforming random variables with 5 practice questions.

Practice Questions

Question 1

If $X$ is a random variable and $Y = X + 5$, what does this transformation do to the distribution of $X$?

Question 2

If $X$ has mean $\mu_X$ and standard deviation $\sigma_X$, what are the mean and standard deviation of $Y = X - 3$?

Question 3

If $X$ is transformed to $Y = 2X$, how does the standard deviation of $Y$ compare with the standard deviation of $X$?

Question 4

Suppose $X$ is a random variable and $Y = -X$. What happens to the distribution of $X$?

Question 5

If $X$ represents the number of heads in $3$ fair coin tosses, which transformed random variable counts the number of tails?