Question

A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are: million from the office building, million from the theater, and million from the parking garage. His profit is zero if he gets no contract. The contractor estimates that the probabilities of getting the office building contract, the theater contract, the parking garage contract, or nothing are , , , and , respectively. Let be the random variable that represents the contractor's profits in millions of dollars. Write the probability distribution of . Find the mean and standard deviation of . Round your answers to three decimal places, if required.

Answer 1

The following are the answer to this question:

Explanation:

In the given question the numeric value is missing which is defined in the attached file please fine it.

Calculating the probability of the distribution for x:

`\to f(x) = 0.19\ for \ x=14\\\\\to f(x) = 0.29 \ for\ x=7\\\\\to f(x) = 0.38\ for \ x=1\\\\\to f(x)=0.14 \ for \ x=0\\`

The formula for calculating the mean value:

`\bold{ E(X)= x * f(x)}`

`=14 * 0.19+7 * 0.29+1 * 0.38+0* 0.14\\\\=2.66 + 2.03+0.38+ 0\\\\=5.07`

`\bold{E(X^2) = x^2 * f(x)}`

`=14^2 * 0.19+7^2 * 0.29+1^2 * 0.38+0^2 * 0.14 \\\\=196 * 0.19+ 49 * 0.29+1 * 0.38+0 * 0.14\\\\= 37.24+ 14.21+ 0.38+0 \\\\=51.83`

use formula for calculating the Variance:

`\to \bold{\text{Variance}= E(X^2) -[E(X)]^2}`

`= 51.83 - (5.07)^2\\\\= 51.83 - 25.70\\\\=26.13`

calculating the value of standard deivation:

Standard Deivation (SD) =
`√(Variance)`

`= √(26.13) \\\\=5.111`