If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Statistics and probability>Unit 9

Lesson 3: Transforming random variables

# Transforming random variables

## Problem

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from each size. Let $X$ represent the shop's profit on a randomly selected pizza. Here's the probability distribution of $X$ along with summary statistics:
SmallMediumLarge
$X=\text{profit ()}$$4$$8$$12$
$P\left(X\right)$$0.18$$0.50$$0.32$
Mean:${\mu }_{X}=\mathrm{}8.56$
Standard deviation:${\sigma }_{X}\approx \mathrm{}2.77$
The company is going to run a promotion where customers get $\mathrm{}2$ off any size pizza. Assume that the promotion will not change the probability that corresponds to each size. Let $Y$ represent their profit on a randomly selected pizza with this promotion.
What are the mean and standard deviation of $Y$?
${\mu }_{Y}=$
dollars
${\sigma }_{Y}\approx$
dollars