Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    How would I go about doing this question? Name:  ImageUploadedByStudent Room1453070079.520693.jpg
Views: 44
Size:  191.2 KB
    Offline

    13
    ReputationRep:
    (Original post by Bruce Harrisface)
    How would I go about doing this question? Name:  ImageUploadedByStudent Room1453070079.520693.jpg
Views: 44
Size:  191.2 KB
    Let's get you started. You are given that the observations are independent of one another - therefore to get the combined likelihood, you simply multiply together the likelihoods for each individual observation. They are all Poisson distributed, so we can simply write down the Poisson likelihood for the x's and the y's.

    \displaystyle L(\alpha | x_{i}) = \frac{e^{-\alpha} \alpha^{x_{i}}}{x_{i}!}

    and

    \displaystyle L(\tau | y_{j}) = \frac{e^{-(\tau + \alpha)} (\alpha + \tau)^{y_{j}}}{y_{j}!}

    Now multiply these together for all the  x_{i} and  y_{j} , and you have the combined likelihood as a function of \alpha, \tau

    The second part of the question simply requires you to (a) set  \tau = 0 in this expression and then differentiate w.r.t.  \alpha to get the maximum likelihood estimate. (b) is similar, but messier. Can you now do (c) yourself?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 18, 2016
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.