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!