GSB 519 Assignment 5

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.]

I353 519 Additional Years of Life for Males .3 $3 31.; 239 '3 HI | "' | 1 Addition Years of Life Probability of Additional Years 2 Beyond Age Zero of Life Beyond Age Zero 3 :4 x} 4 0.5 0.00?51 5 1 .5 0.00056 6 2.5 0.00038 7 3.5 0.00029 8 4.5 0.00024 9 5.5 0.00013 10 6.5 0.0001? 1 1 ?.5 0.00015 12 8.5 0.00018 I _| 1 3 9.5 0.00018 14 10.5 0.00018 1 5 1 1 .5 0.00018 16 12.5 0.0002 17 13.5 0.00025 18 14.5 0.00032 13 15.5 0.0004800?3 20 16.5 0.0006855T3 21 1?.5 0.000917326 22 18.5 0.001133153 23 19.5 0.00135626 24 20.5 0.00133349 25 21.5 0.0014T2586 26 22 .5 0.001402542 27 23 .5 0.001352221 28 24 .5 0.001358885 29 25 .5 0.0012828?6 30 26 .5 0.00134TT43 31 2? .5 0.001237042 32 28.5 0.001358564 33 29,5 0,001318775 34 30,5 0,001378847 35 31,5 0,001359142 36 32,5 0,001408642 37 33,5 0,001545099 38 34,5 0,001634408 39 35,5 0,001793465 40 36,5 0,001830896 41 37,5 0,002058594 42 38,5 0,002218989 43 39,5 0,002318003 44 40,5 0,002497214 45 41,5 0,002625624 46 42,5 0,002829616 47 43,5 0,003127286 48 44,5 0,003371848 49 45,5 0,00363289 50 46,5 0,003865731 51 47,5 0,004286488 52 48,5 0,004594853 53 49,5 0,004860601 54 50,5 0,005204666 55 51,5 0,005403102