# Probability density function for cost

The actual cost of a system, X, in $50,000, is predicted by the probability density function

f(x) = { 0.5 - |0.5-0.25x| for 0 <= x <= 4 and 0 otherwise

1. What is the expected cost to system?

2. What is the cost Xs of system for which the probability of exceeding Xs is 0.01?

https://brainmass.com/statistics/probability-density-function/probability-density-function-cost-540209

#### Solution Preview

f(x) ={ 0.5 - |0.5-0.25x| for 0 <= x <= 4 and 0 otherwise

OR

f(x) =

0.5 - 0.5+0.25x == 0.25x for 0 <= x < 2

and

0.5 + 0.5 - 0.25x == 1.0 - 0.25x for 2 <= x <= 4

and

0 otherwise

1.

E(X) = integration(0 to 4) {x.f(x).dx}

=> E(X) = integration(0 to 2) {x.f(x).dx} + integration(2 to 4) {x.f(x).dx}

=> E(X) = ...

#### Solution Summary

For given probability density function, expected cost is estimated. Also, for given probability, cost is estimated.

$2.19