Poisson distribution-solve for x

[fysiikka111]

Homework Statement

How to find for a Poisson distribution the number of successes for a given probability and mean. For example, for mean, $\lambda$, of 1, and a required probability of 0.01, what would the number of successes in the time interval be?

Homework Equations

$$Pr(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!}$$

The Attempt at a Solution

Not sure how to rearrange to solve for x. Or is there a different approach?

 

[Mark44]

Homework Statement

How to find for a Poisson distribution the number of successes for a given probability and mean. For example, for mean, $\lambda$, of 1, and a required probability of 0.01, what would the number of successes in the time interval be?

Homework Equations

$$Pr(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!}$$

The Attempt at a Solution

Not sure how to rearrange to solve for x. Or is there a different approach?

Solve the equation .01 = e^-11^x/x! for x.

I would just pick values of x and see if the expression on the right equals .01.

 

[fysiikka111]

Thanks. How would you get rid of the factorial?

 

[Mark44]

You replace it with its value. For example, if you pick x = 3, 3! = 6.

 

[Ray Vickson]

Since x is an integer in the Poisson distribution, there might not be an exact solution. For example, if lambda = 1 and the required probability is p = 0.01, Maple gets x = 4.278021, by interpreting x! in terms of a Gamma function. The actual p-values at x = 4 and x = 5 are 0.0153283 and 0.0030657, respectively.

RGV