Answer to Question #224446 in Statistics and Probability for Qasim

Question

A large industrial firm purchases several new word processors at the end of each year, the exact number depending on the frequency of repairs in the previous year. Suppose that the number of word processors,

X, purchased each year has the following probability distribution:

X 0 1 2 3

P(X=x) 1/10 3/10 2/5 1/5

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50X2 dollars will be issued, how much can this firm expect to spend on new word processors during this year?

Answer 1

The amount this firm can expect to spend on new word processors during this year is calculated as follows:

$E\left(X\right)=\left(1\times \frac{3}{10}\right)+\left(2\times \frac{2}{5}\right)+\left(3\times \frac{1}{5}\right)$

$E\left(X\right)=1.7$

$E\left(X^2\right)=\left(1^2\times \:\frac{3}{10}\right)+\left(2^2\times \:\frac{2}{5}\right)+\left(3^2\times \:\frac{1}{5}\right)\:$

$E\left(X^2\right)=3.7$

$Expense=E\left(1200x-50x^2\right)$

$Expense=E\left(1200x\right)+E\left(-50x^2\right)$

$Expense=1200E\left(x\right)-50E\left(x^2\right)$

Therefore:

$Expense=\left(1200\times 1.7\right)-\left(50\times 3.7\right)=1855$