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Help with Poisson Distribution - Find Mean and Variance

The Duke of Moral Hazard · 2014-05-19 21:36:08

Having trouble with some revision regarding the Poisson Distribution, question as follows has me stumped: (i) Let X ~ Poisson(10) and Y ~ Poisson(4). If X and Y are independent, find the mean and variance of the RV Z = 2X + 3Y (ii) For the RV X in (i), find p(8<=X=<13) Any help welcomed.

19-05-2014 10:36PM

#1

The Duke of Moral Hazard

Registered Users, Registered Users 2 Posts: 55 ✭✭

Join Date: May 2011

Posts: 47

Having trouble with some revision regarding the Poisson Distribution, question as follows has me stumped:

(i) Let X ~ Poisson(10) and Y ~ Poisson(4).

If X and Y are independent, find the mean and variance of the RV Z = 2X + 3Y

(ii) For the RV X in (i), find p(8<=X=<13)

Any help welcomed.

0

Comments

#2 20-05-2014 11:56PM

Yakuza

Registered Users, Registered Users 2 Posts: 5,130 ✭✭✭

Join Date: November 1999

Posts: 4999

i) You can combine multiple (independent) Poisson dists, the resulting dist has a parameter equal to the total of the components of the sum.
ii) To find the probability of a region between two points, look up cumulative poisson tables for Poisson(10) at the two points and subtract, or work out the sum of λ^k * exp(-λ) / k! where k = 9 to 13 (and λ = 10).

0