What is the standard deviation of the payoff from an investment that yields $1,000,000 with a probability of 0.001 and $0 with a probability of 0.999?
A) $998,001,000
B) $999,000
C) $316.07
D) $31,606.96

Question

Quizplus · Accepted Answer

The standard deviation of a discrete random variable is calculated using the formula $\sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)}$, where $x_i$ are the values the variable can take, $P(x_i)$ are the probabilities of these values, and $\mu$ is the expected value. The expected value ($\mu$) of the investment is $0.001 \times 1,000,000 + 0.999 \times 0 = 1,000$. The variance is $(1,000,000 - 1,000)^2 \times 0.001 + (0 - 1,000)^2 \times 0.999 = 999,000,000$. The standard deviation is the square root of the variance, which is $\sqrt{999,000,000} = 31,606.96$.

What Is the Standard Deviation of the Payoff from an Investment