Please help... Can someone please explain to me, in as much detail as possible,

Question

Please help... Can someone please explain to me, in as much detail as possible, how the data points in the yellow highlighted column circled in red, is the pdf of X. How did my teacher come up with those numbers as the answer? Also, the green column circled in purple, why is that part of the solution? Please help explain all of this. I am really trying to understand. Please type your answer. I have a hard time reading other people's handwritting sometimes.

Insert Draw Page Layout Formulas Data Review View Foot PDF ACROBAT Q Tell me what you want to do File Home d Cut Condit Merge & Center B I U Format painter Clipboard Font Numb G29 An insurance company offers its policy holders different payment options, which includes paying 21 various time between payments, in months. Hence a random variable can be defined as X- number of months between two payments. 22 The cumulative distribution functio (CDF) of X give as 0.45 sx

Explanation / Answer

a) Probability density function x f(X) x*f(X) X^2 *f(X) 1 0.3 0.30 0.30 3 0.1 0.30 0.90 4 0.05 0.20 0.80 6 0.15 0.90 5.40 12 0.4 4.80 57.60 b) v(x) =E(x^2) -(E(x))^2 where E(x^2) = 65 E(x) = 6.5 v(x)= 22.75 c) p(2

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