Originally Posted by

**Tau** 1.

[snip]

2.

Decide the value of *k* so the function $\displaystyle f(x) = k \cdot x \cdot e^{\frac{-x^2}{2a^2}}$ $\displaystyle , x > 0 (\sigma > 0)$ becomes the density function for the random variable $\displaystyle X$.

Then calculate $\displaystyle P(X > \sigma)$. (Rayleigh distribution)

3.

On average, 5.2 hurricanes occur in a year. What is the probability three or less will occur this year?

We can assume that the number of hurricanes can be approximated with a Poisson random variable.

Thank you.