Question

An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and 15, respectively. Determine the mean and variance of the worth of the investment.

Answer 1

for any discrete random variable the expectation is:

E(X) = µ = ?x * P(X = x)

the variance of a discrete random variable is:

Var(X) = s² = ?(x - µ)² * P(X = x) = {?x² * P(X = x) }- µ²

the standard deviation is just the square root of the variance.

Let X be the investment worth. The mean is:

E(X) = 1,000 * 0.25 + 2,000 * 0.60 + 5,000 * 0.15 = 2,200

the variance is:

Var(X) = 1,000^2 * 0.25 + 2,000^2 * 0.60 + 5,000^2 * 0.15 - 2,200^2
Var(X) = 1,560,000