# Thread: a question about the standard deviation of the function of a random variable

1. ## a question about the standard deviation of the function of a random variable

Hi all,

I'm having trouble with the last part of this question:
I have the profit formula g(X) as a function of X the random variable determined by the cost of the further work:

g(X)=1.1X + 1.1(20)

g(X)=1.1X + 22

so E(g(X))=1.1(4) + 22 = 26.4million

the s.d is the root of the variance var(g)= (a^2)(var(X)) for aX+b

so my calculations give the variance as (1.1^2)(1^2) = 1.21

so s.d = 1.1 million

but the answer in the back of the book is 1million.

Would someone be able to tell me where I am going wrong???
Many thanks!

2. ## Re: a question about the standard deviation of the function of a random variable

Hey flashylightsmeow.

The profit will be 10% of his expected costs, so if the expected cost is say h(X), then g(X) will be 0.1*h(X). Retry the problem by getting the profit function as a separate function of the total costs (the profit (remember the profit will be 10% of the costs so if the total cost is to be 100 million, then the profit will be 10 million).

3. ## Re: a question about the standard deviation of the function of a random variable

Dear Chiro, thank you very much for your help!!