Purchase Solution

Probability Distributions

Not what you're looking for?

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

Solution Summary

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

Solution Preview

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 ...

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.