Stat 231; Fall 2013. Assignment 1

Instructors: Schonlau/ Banerjee

Due date: Monday, 30 Sep, 2013 at noon

This assignment consists of two parts:

a) likelihood questions 1+2

b) online quiz related to descriptive statistics/ graphs.

Upload your solution to the likelihood questions into the online course Dropbox

by the due date (Please use either a pdf or a word document). They will be

marked online.

For the quiz you have 3 attempts (3 times pressing the submit button. One

attempt can stretch over several days. You can save the quiz and continue on a

different day. The highest attempt will be recorded.

There are no course grades associated with the assignment. We record the

theoretical grades only to see which questions are difficult for you and how many

students participate.

1) Suppose we have a Bernoulli r.v (

π

), where

π

is the probability of

success.

Let X = number of trials before the 1st success occurs.

Given a data set

{x

1

,x

2

,....x

n

}

where each xis are independent draws from

the r.v X as defined above,

(a) Construct the likelihood function

(b) Construct the log-likelihood and the relative likelihood function.

(c) Find the MLE for

π

.

2) (more challenging) Suppose

{x1,x2,....xn}

is an independent sample drawn

from the random variable X, where X follows an uniform distribution, i.e.

X~U(0,

θ

)

, where θ is the unknown parameter.

a) Write down the likelihood function based on your observations.

b) Find the MLE for θ.

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