Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $X \sim N(\mu,\sigma^2)$ and $$f_X(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}.$$ where $-\infty < x < \infty$.

Express $\operatorname{E}(aX + b)$ and $\operatorname{Var}(aX +b)$ in terms of $\mu$, $\sigma$, $a$ and $b$, where $a$ and $b$ are real constants.

This is probably an easy question but I'm desperate at Probability! Any help is much appreciated as I'm not even sure where to start.

share|improve this question
2  
If you're studying this, then surely you have access to formulas relating $E(aX+b)$ to $E(X)$? –  Gerry Myerson Aug 12 '12 at 12:52
    
@GerryMyerson I have seen those formulas before but I think I was more so thrown off at the question as it was going for the same amount of marks as trickier ones. Also I don't have many 'useful' notes in this subject. It seems ridiculously easy now. –  Fred Aug 12 '12 at 18:41

2 Answers 2

up vote 2 down vote accepted

If $a,b$ are constants, i.e. not random, then $$ \mathbb{E}(aX+b) = a\mathbb{E}(X)+b, $$ $$ \operatorname{var}(aX+b) = a^2 \operatorname{var}(X). $$

Now plug in $\mu$ and $\sigma^2$ in the appropriate places.

share|improve this answer
    
Oh wait so aμ + b, (a^2)(σ^2)? I'm being completely thrown off by these exam questions because some are difficult and some easy but worth the same amount of marks. Thanks so much anyway! :) –  Fred Aug 12 '12 at 17:29

Not an answer:

Check out Wikipedia, and then learn them through comprehension and by heart.

  1. Normal Distribution (E, $\sigma$ included)

  2. What is Variance

  3. Important Properties of Variance

  4. Important Properties of Expected Value

share|improve this answer
    
Upvoted! $ $ $ $ –  Did Aug 12 '12 at 14:03
    
@did Ahah! And finally I knew the secret of posting strings that satisfy strlen(string) < 15! –  FrenzY DT. Aug 12 '12 at 14:05
    
I like your answer, but I think letting the first link be a (very) comprehensive article about the normal distribution, from which he only needs to extract what the mean and variance of a normal distribution, might be a bit discouraging. (Given the difficulty of the question). –  Henrik Aug 12 '12 at 15:55
    
@Henrik: Sorry but your conjecture is now disproved, see which answer got accepted. –  Did Aug 12 '12 at 17:34
    
@FrenzY Thanks for your answer. I found the formulas that were given above in the articles. Although was a bit confusing! –  Fred Aug 12 '12 at 18:33

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.