Repairs The probability model below describes the number of...

Repairs The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. $$\begin{array}{|c|c|c|c|c|}\hline{\text { Repair Calls }} & {0} & {1} & {2} & {3} \\ \hline \text { Probability } & {0.1} & {0.3} & {0.4} & {0.2}\\ \hline \end{array}$$ a) How many calls should the shop expect per hour? b) What is the standard deviation?

Repairs The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.
$$\begin{array}{|c|c|c|c|c|}\hline{\text { Repair Calls }} & {0} & {1} & {2} & {3} \\ \hline \text { Probability } & {0.1} & {0.3} & {0.4} & {0.2}\\ \hline \end{array}$$
a) How many calls should the shop expect per hour?
b) What is the standard deviation?

Key Concepts

Discrete Random Variable

A discrete random variable is a variable that can take on a countable number of distinct values, each associated with a particular probability. In probability theory and statistics, it is used to model outcomes that occur in discrete steps or counts, such as the number of events happening in a given period.

Probability Distribution

A probability distribution describes how probabilities are assigned to the possible values of a discrete random variable. It provides the framework for understanding the likelihood of different outcomes. In the context of discrete events, the probabilities sum to one and allow the computation of various statistical measures.

Expected Value

The expected value of a discrete random variable is a measure of its central tendency, calculated by summing the products of each possible value and its corresponding probability. It represents the long-run average or mean value one would expect if the experiment were repeated many times.

Variance and Standard Deviation

Variance measures the spread or dispersion of a discrete random variable’s values around the expected value, computed by summing the squared differences between each value and the mean, each weighted by its probability. The standard deviation is the square root of the variance and provides a scale-sensitive measure of spread, indicating how much the values typically deviate from the mean.

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