An investment will pay $2,000 a quarter of the time; $1,600 half of the time and $1,400 a quarter of the time. The standard deviation of this asset is:
A) $600
B) $1,650
C) $47,500
D) $217.94

Question

Quizplus · Accepted Answer

The expected value (mean) of the investment is calculated as follows: E(X) = (0.25 * 2000) + (0.5 * 1600) + (0.25 * 1400) = 500 + 800 + 350 = $1650. Then, we calculate the variance: Var(X) = (0.25 * (2000 - 1650)^2) + (0.5 * (1600 - 1650)^2) + (0.25 * (1400 - 1650)^2) = (0.25 * 350^2) + (0.5 * 50^2) + (0.25 * 250^2) = 30625 + 1250 + 15625 = 47500. The standard deviation is the square root of the variance, √47500 = $217.94.

An Investment Will Pay $2,000 a Quarter of the Time;