Let x represent the number of times a customer visits a...

Let $x$ represent the number of times a customer visits a grocery store in a 1 -week period. Assume this is the probability distribution of $x$ : $$\begin{array}{l|cccc}x & 0 & 1 & 2 & 3 \\\hline p(x) & .1 & .4 & .4 & .1\end{array}$$ Find the expected value of $x$, the average number of times a customer visits the store.

Let $x$ represent the number of times a customer visits a grocery store in a 1 -week period. Assume this is the probability distribution of $x$ :
$$\begin{array}{l|cccc}x & 0 & 1 & 2 & 3 \\\hline p(x) & .1 & .4 & .4 & .1\end{array}$$
Find the expected value of $x$, the average number of times a customer visits the store.

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Key Concepts

Expected Value

The expected value, also known as the mean, of a random variable is a measure of the central tendency that provides the long-run average outcome of a random process. It is calculated by multiplying each possible value by its probability and then summing these products. This provides a weighted average that summarizes the overall distribution of the variable.

Discrete Random Variable

A discrete random variable is a variable that can take on a countable number of distinct values. In probability and statistics, these are used to model outcomes that arise from specific, separate events, such as the number of visits to a store. Each outcome has an associated probability, with the sum of all probabilities equaling one.

Probability Distribution

A probability distribution describes how the probabilities are assigned to the different possible values of a random variable. In the context of a discrete random variable, the probability distribution is often presented in a table or a list where each possible value is paired with its corresponding probability.

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