Thread: Probability sum question

Would someone be able to simplify the following;

Sum(from i=1 to N(t)) of X(i,t)


where N(t) is a poisson distributed random variable with mean 4.5
Each X(i,t) is an independent log-normal varibles with mean and variance of 20,000
need to repeat for each t = 1,2,3

I don't need this solved, just in a form where it can written into excel to be evaluated.

Also from about the 40 of the 150ish people I asked in my class about this, not one of us has even a slight clue as to how to do this

thanks

Originally Posted by Aaron1097

Would someone be able to simplify the following;

Sum(from i=1 to N(t)) of X(i,t)


where N(t) is a poisson distributed random variable with mean 4.5
Each X(i,t) is an independent log-normal varibles with mean and variance of 20,000
need to repeat for each t = 1,2,3

I don't need this solved, just in a form where it can written into excel to be evaluated.

Also from about the 40 of the 150ish people I asked in my class about this, not one of us has even a slight clue as to how to do this

thanks

What do you mean by evaluated, its a random variable. Do you mean code a random number generator that returns a instantiation of the Rv, or something else?

CB

Sorry for the miss-statement, I haven't actually been taught compound poisson, but apparently am expected to know and understand it.

What I am after is the expected values and the variance, which I believe I can now evaluate, (though this is based only on what I have read of wikipeadia, so im not sure how correct this is)

Originally Posted by Aaron1097

Sorry for the miss-statement, I haven't actually been taught compound poisson, but apparently am expected to know and understand it.

What I am after is the expected values and the variance, which I believe I can now evaluate, (though this is based only on what I have read of wikipeadia, so im not sure how correct this is)

The expected value can be calculated using Wald's Equation: Wald's equation - Wikipedia, the free encyclopedia

The variance can be calculated using a modified argument.