9.3 Properties of Expected Values

We often add a constant to a random variable or multiply a random variable by a constant. For example, suppose the computer shipper in 4M Analytics 9.1 has to pay fee of $1,000 to an agent who found this customer. In this case the net profits are not X dollars, but X - $1,000. Similarly, we often multiply random variables by constants. The car shop that sells tires makes a sale of Y tires to a customer. If the shop charges $5 to mount each tire, then the mounting charge for a sale of Y tires is $5 × Y.

What are the mean and standard deviation of these quantities? We don’t need to start over by defining a new random variable. An easier approach uses the properties of the random variables that we already have. ...

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