If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)

Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie

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: 5,141 ✭✭✭

Join Date: November 1999

Posts: 5008

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