By investing in a particular stock, a person can make a profit in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?

Expected gain of person is $500.

Explanation:

Amount of profit to make=$4000

Probability of making $4000 profit=0.3

Amount of loss=$1000

Probability of loss=0.7

To Find:

What is this person’s expected gain?

Solution::

Let say Z denotes the gain then Z has two values +4000 and -1000.

(+ve sign for gain and -ve for loss)

By using the formula for expected value of discrete random variable.

where:

f(z) is the probability.

E(Z)=4000(0.3)+(-1000*0.7)

E(Z)=$500

Expected gain of person is $500.