A shareholder believes that in one year, there is a 20% chance that his stock will be worth $75, a 50% chance that it will be worth $100, and a 30% chance that it will be worth $140.
a. Find the stock's expected value in one year.
b. Find the standard deviation of the stock's worth in one year.

Question

Quizplus · Accepted Answer

The Answer is a. E(X) = Σ xP(x) = $75(0.20) + $100(0.50) + $140(0.30) = $107
b. σ = SD(X) =

a. E(X) = Σ xP(x) = $75(0.20) + $100(0.50) + $140(0.30) = $107 b. σ = SD(X) = , Var(X) = Σ (x - μ)2 P(x) Var(X) = Σ(x - μ)2 P(x) = (75 - 107)2(0.20) + (100 - 107)2(0.50) + (140 - 107)2(0.30) = 556 σ = SD(X) = = = $23.58

, Var(X) = Σ (x - μ)2 P(x)
Var(X) = Σ(x - μ)2 P(x) = (75 - 107)2(0.20) + (100 - 107)2(0.50) + (140 - 107)2(0.30) = 556
σ = SD(X) = a. E(X) = Σ xP(x) = $75(0.20) + $100(0.50) + $140(0.30) = $107 b. σ = SD(X) = , Var(X) = Σ (x - μ)2 P(x) Var(X) = Σ(x - μ)2 P(x) = (75 - 107)2(0.20) + (100 - 107)2(0.50) + (140 - 107)2(0.30) = 556 σ = SD(X) = = = $23.58

=

= $23.58

A Shareholder Believes That in One Year, There Is a 20