# Probability Distributions

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An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having p.m.f.

.9 x=0

f(x) = {

(C/x) x=1,2,3,4,5,6 (where C is a constant)

Determine C and the expected value the insurance company must pay

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The solution contains the determination of the constant and Expected value of a probability density function. Step by step calculations are provided.

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Please see the attachment for solution. If you need any further clarification about this problem please ask me. Thank you.

Since f(x) is a p.m.f., we have

That is,

f(0) + f(1) + f(2) + f(3) + f(4) + f(5) + f(6) =1

i.e., 0.9 + (C/1) + (C/2) + (C/3) + (C/4) + (C/5) + (C/6) = 1

i.e., 0.9 + C{1 + (1/2) + (1/3) + (1/4) + (1/5) + (1/6)} = 1

i.e., 0.9 + C{(60+30+20+15+12+10)/60} = 1

i.e., 0.9 + C(147/60) = 1

i.e., C(147/60) = 1 - 0.9 = 0.1

i.e., 147*C = 60*0.1 = 6

i.e., C = 6/147 = 2/49

Thus the constant, C ...

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