For determining the half=lives of radioactive isotopes, it is important to know what the background radiation is in a given detector over a period of time. Data taken in a y-ray detection experiment over 300 one-second intervals yielded the following data:

Data......Frequency

0 ............. 17

1 ............. 47

2 ............. 63

3 ............. 63

4 ............. 49

5 ............. 28

6 ............. 21

7 ............. 11

8 .............. 1

a) Do these look like observations of a Poisson variable with mean $\displaystyle \lambda=3$?

I calculated the sample mean by: (0*17+1*47+2*63+3*63+4*49+5*28+6*21+7*11+8*1)/300=303/100=3.03

and sample variance by:

$\displaystyle

(0-3.03)^{2}*(17/300)+(1-3.03)^{2}*(47/300)+...+

$(8-3.03)^{2}*(1/300)=43744099/12000000=3.18

b) Construct a probability histogram with $\displaystyle \lambda=3$ and a relative frequency histogram on the same graph. I'm not sure how to find the values for the histogram. I am not sure how to read the poisson table because the amounts I calculate are different than the ones on the chart when I use $\displaystyle (\lambda^{x}e^{-\lambda})/x!$