Question

1)An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $30,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the investment will result in a loss of $30,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 20% probability the economy will slip into recession.

What is the expected profit from this investment?

Answer 1

Concepts and reason

Discrete variable: A variable is said to be discrete variable, if it is countable.

Probability mass function: Probability mass function is the probability function for discrete random variable. For a discrete random variable X, the mass function is.

Discrete probability distribution function: If the random variable in the distribution is discrete random variable that is countable and space exists between each possible outcomes and all the outcomes are completely restricted to the whole numbers and the integer values; then the probability distribution of the random variable is discrete distribution.

Expected value: Expected value is calculated by the sum of each values of X multiplied by the probability mass function. It is denoted by.

Fundamentals

The probability mass function is defined as,

For the discrete variable, all the outcomes are either whole numbers or integers.

Formula for expected value is .

The probability mass function is obtained below:

Let X is denoted as the investment that results in profit/loss, is denoted as the probability of the investment will results strong or slip.

From the given information, the investment will result in a profit of $30,000 with 20% probability, the investment will result in a profit of $10,000 with 60% probability, and the investment will result in a loss of $30,000 with 20% probability. Thus, the possible values of X are 30,000, 10,000 and 30, 000.

The distribution for the random variable X is given by,

The expected profit from this investment is obtained below:

Ans:

The expected profit from this investment is $6,000.