The Expected Value

In the box below, please enter the mean of the distribution given above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

Your guess:

You got the correct answer of E[X] = 11.1. Congratulations!

Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.

Show Formula

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For the Binomial distribution, the formula for the expected value (mean) is

In this formula, there are a few symbols to know:

Show Solution

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Show the R Code

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Copy and paste the following code into your R script window, then run it from there.

In the R output, the number given after running the final line above is the mean of the distribution, the expected value of the random variable. This code is designed to encourage you to see the connection between the Binomial distribution and all other finite discrete distributions. In R, you could perform the calculation much more quickly: 15*0.74. But, that connection is not evident.

Show the Excel Code

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Copy and paste the following code into your Excel spreadsheet window, making sure the value x ends up in A1 after pasting.

When copying this table to Excel, you may want to highlight this note. It seems to help ensure that the code starts in cell A1.