Let X represent number of times someone went to a bagel store in one month. Assume...

Let X represent number of times someone went to a bagel store in one month. Assume that the following table is the probability distribution of X: a. What are the “expected value” and “standard deviation” of X?

X 0 1 2 3

P(X) 0.10 0.30 0.40 0.20

Question: If I were to compute the conventional mean of X, my answer would be X=1.5. Why does the answer in (a) differ?

Solutions

Expert Solution

Consider the following table:

The population mean is calculated as follows:

And finally, taking the square root to the variance we get that the population standard deviation is

Since the probability distribution of the variable is given, the way of calculating the mean differs. We basically take the weighted average of the variable where the weights are the probability in order to calculate the mean when the probability distribution is given. It is, in short, the weighted average.

The conventional mean of X is basically the simple average.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

orchestra answered 1 year ago

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