Let X equal an integer selected at random from the first m positive integers, {1, 2, ..

Chapter 2, Problem 2.3-7

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QUESTION:

Let X equal an integer selected at random from the first m positive integers, {1, 2, ... , m}. Find the value of m for which E(X) = Var(X). (See Zerger in the references.)

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QUESTION:

Let X equal an integer selected at random from the first m positive integers, {1, 2, ... , m}. Find the value of m for which E(X) = Var(X). (See Zerger in the references.)

ANSWER:

Step  1 of 5

 =integer selected at random from the first  positive integers

Since we random select one of the first  positive integers, each integer from the set  is equally likely and thus we have 1 chance in  of selecting each integer:

Step  2 of 5

The expected value (or mean) is the sum of the product of each possibility  with its probability  

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