Poisson Distribution

[Starling]

So here is a problem that I was given and I'm pretty lost on:

P(x) = e^-L L^x/x! , for L= 7.2

a) Plot histogram
b) Find mode, mean, median, standard dev.
c) Pr(x>or equal to 8) =? Hint: 1-Pr(x<8)


I got this far lol:

P(x) = e^-7.2 L^7.2
-----------------------------
x!

Any help would be much appreciated! Thanks in advance

 

[tkhunny]

I'm a little puzzled by this definition. You say it's Poisson, but fail to define it ONLY on the Whole Numbers. x = 0, 1, 2, ... -- Something like that.

Once you've done that, the rest is pretty simple.

Start with x = 0, giving \(\displaystyle Pr(0)\,=\,\frac{e^{-7.2} * 7.2^{0}}{x!}\,=\,e^{-7.2}\)

It is important to note that this portion of the function is independent of the changing value of the variable, x.

x = 1 gives \(\displaystyle Pr(1)\,=\,Pr(0)*\frac{7.2^{1}}{1!}\)

Each successive value can be calculated quickly from the previous.

\(\displaystyle Pr(n+1)\,=\,Pr(n)*\frac{7.2}{n+1}\)

There are important properties of the Poisson that you should be able to exploit, such as Mean = Variance = L and Mode = [L]

http://en.wikipedia.org/wiki/Poisson_distribution

 

[Starling]

Ok thank you tkhunny! I can work with that