1. Open the Excel file GSB 519 Additional Years of Life for Males. The random variable x =.5, 1.5, 2.5,.....,110.5, where x denotes additional years of life beyond age zero. The second column shows the probability that each specific value of x occurs. This column contains the probability mass values, f(x). For example, the probability that a new-born male baby will live 20.5 years (not less or not more) is .00133349, i.e., f(20.5) = .00133349. Find the following properties of the random variable x.

a. mean

b. median

c. mode

d. variance

e. standard deviation

f. skewness

g. kurtosis

h. coefficient of variation

i. Find the value of the distribution function F(x) when x = 65.5.

j. How much total probability is contained within two standard deviations of the mean?

[You should use Excel in order to avoid hand calculations. However, do not use Excel commands like AVERAGE or STDEV; you will get incorrect answers if you do.]