## Question 896:

1

1. Q896_1_q896-randomvariable.xls
The mean of a random variable is the same thing as the expected value over the long term. To find it you simply sum the values of x times their probability of occurrence. See the attached spreadsheet for the calculations.  For the first value, the expected value is 2*.15 = .3 and so on.  When you add up all the expected values you get 6.30 which is the answer to part a.

The standard deviation can be found by
1. Squaring the mean value we found in part a 6.30*6.30 = 39.690
2. Summing up all the deviations which can be found by squaring the X column value and multiplying it times the P(X) column. So for the first one the deviation value is 2*2*.15  = .6.
3. Next we add up all the deviations and we get 47.4
4. Next we find the variance which is found as the sum of deviations - mean squared = 47.4-39.690 = 7.710
5. Finally we take the square root of the variance to get the standard deviation = SQRT(7.710) = 2.777
So the standard deviation and answer to part b is 2.777