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### Course: AP®︎/College Statistics>Unit 8

Lesson 2: Mean and standard deviation of random variables

# Mean (expected value) of a discrete random variable

You might need: Calculator

## Problem

A construction company is considering submitting bids for two contracts. It will cost the company $\mathrm{}10,000$ to prepare and submit the bids, and if won, each bid would produce $\mathrm{}50,000$ of income to the company. The company estimates that it has a $10\mathrm{%}$ chance of winning any given bid.
Here is the probability distribution of $X=$ the number of bids the company wins, and $M=$ the amount of money the company profits from the bids.
$0$$1$$2$
$M=\text{profit}$$-\mathrm{}10,000$$\mathrm{}40,000$$\mathrm{}90,000$
Probability$0.81$$0.18$$0.01$
Calculate the mean of $M$.
${\mu }_{M}=$
dollars