Hi guys thanks for your help earlier.

Have just a few more that perhaps you could help me check.

First of all i have a question that states :

Suppose that the number of cracks per concrete specimen for a particular type of

cement mix, X say, has approximately a Poisson probability distribution. Further-

more, assume that the average number of cracks per specimen is 2.5.

q1) what are the chances of the number of cracks being 5 given that the number of cracks is an even number.

A) now obviously this is impossible so there is 0 chance.

the next bit is where it gets tricky.

Q2)

Find the probability that a randomly selected concrete specimen has 6 cracks

given that the number of cracks on the specimen is an even number.

A) now if you simply put the numbers into poissons you come out with 0.02783

now i was told by my lecturer that this is not correct as i have not taken the chances of it being even into account. So any help on this would be helpful.

also i have a question and have no idea where to start so any specific points or help would be really greatful.

So the real toughy is :

In a photoelectric detector, the number of photoelectrons

*Y *produced in time t

depends on the (normalized) incident energy

*X*. If *X *were constant, say, *X *= *x*,

Y

would be a Poisson random variable with mean *x*, but as real light sources {

except for gain-stabilized lasers { do not emit constant energy signals, *X *must be

treated as a random variable. In certain situations *X *takes ¯nite number of values

with probability mass function given by

P

(*X *= *xi*) = *pi; i *= 1*; : : : ; m:*

Show that the average value of photoelectrons

*Y *equals to the average value of the

incident energy *X*, i.e.

*E*(*Y *) = *E*(*X*)*:*

*now im completely clueless on how to do this so some help would really be helpful as im lost*

*Cheers guys and gals!*

* *