Theory of estimation lecture notes PDF

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Very nice guide questions that will help you prepare adequately for your cats and exams.A very good reference material....

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Theory of estimation. Kenyatta university. Answer all questions and remember to write your name and registration number Q1 Use matrix notation to fit a quadratic equation

y =α 0 + α 1 x +α 2 x

2

using the following five data points: x

-3

-1

0

1

3

y

1

0

1

1

3

Q2 A random sample

X 1 , X 2 , . .. .. X n

of size n is taken from a

population whose probability density function given by 1 1 exp ( − ( x −5 )2 ,−∞ < x < ∞ 4θ 2 √ πθ 0 , elsewhere ¿ f ( x , θ ) =¿ { ¿ ¿ ¿ ¿

where

θ

is a positive constant. Identify this distribution and state its

mean and variance. Obtain the maximum likelihood estimator of θ and examine it for unbiasedness , consistency and sufficiency. Q3

The random variable X has uniform distribution over the interval (

λ−θ , λ + θ ) where λ

and

θ are parameters. Obtain the moment estimators of

λ

and θ . If a random sample of five values is taken from such a population, evaluate the moment estimates of λ 1, 4 and 2.

and θ

given that the five values are 5, 3,...