Variance and Standard Deviation of a Random Variable
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Variance and Standard Deviation of a Random Variable

Variance and Standard Deviation of a Random Variable

[From: ] [author: ] [Date: 11-05-31] [Hit: ]
and how you got that answer?Before planting a crop for the next year, a producer does a risk assessment. According to her assessment, she concludes that there are three possible net outcomes: a $7,000 gain,......
Could someone here maybe explain the answer to this question, and how you got that answer?

Before planting a crop for the next year, a producer does a risk assessment. According to her assessment, she concludes that there are three possible net outcomes: a $7,000 gain, a $4,000 gain, or a $10,000 loss with probabilities 0.55, 0.20, and 0.25, respectively.

What is the variance and standard deviation of the random variable?

-
Variance = E(X^2) - [E(X)]^2
Where E(X^2) = SUM of x^2 * P(x) for all x, and similarly E(X) = SUM of x * P(x) for all x

x = the gain or loss outcomes
P(x) = the probability of that outcome

E(X) = 0.55*7000 + 0.2*4000+0.25*-10000 = 2150
E(X^2) = 0.55*7000^2+0.2*4000^2+0.25*(-10000^2) = 55,150,000
Variance = 55,150,000 - (2150^2) = 50,527,500
Standard deviation is the square root of variance or = 7108.269

Alternative method:

Variance = SUM of P(x)*(x-mean)^2
= 0.55(7000-2150)^2+0.2*(4000-2150)^2+0.25…
1
keywords: and,Variable,Standard,Deviation,Random,Variance,of,Variance and Standard Deviation of a Random Variable
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .