# Stats first year help

• Aug 20th 2010, 03:27 AM
fancynick
Stats first year help
Hello, i am preparing for my Statistics examination and would like to ask help with the questions i struggle.

http://img17.imageshack.us/img17/5141/73988751.jpg

http://img44.imageshack.us/img44/4715/39539677.jpg

Am i right with these two?

http://img51.imageshack.us/img51/1503/question1l.jpg

http://img189.imageshack.us/img189/905/question2x.jpg

Would appreciate if You could help with any of these.
• Aug 22nd 2010, 11:15 AM
CaptainBlack
Quote:

Originally Posted by fancynick
Hello, i am preparing for my Statistics examination and would like to ask help with the questions i struggle.

http://img17.imageshack.us/img17/5141/73988751.jpg

The pdf is:

$f(x)=\begin{cases}
\theta e^{-\theta x}& , x>0\\
0& , \text{otherwise}
\end{cases}$

and the sketch looks OK

CB

..
• Aug 22nd 2010, 11:31 AM
CaptainBlack
Quote:

Originally Posted by fancynick

$\displaystyle E(x)=\int_{x=0}^{\infty} x\, \theta e^{-\theta x}\; dx$

so:

$\displaystyle E(x)=\left[-\dfrac{\left( \theta\,x+1\right) \,{e}^{-\theta\,x}}{\theta}\right]_{x=0}^{\infty}=\frac{1}{\theta}$

CB