i) Derive method of moments and maximum-likelihood estimators for parameter µ based on a sample of size n from a Normal distribution having known variance σ2 and unknown mean µ. Compute your...

i) Derive method of moments and maximum-likelihood estimators for parameter µ

based on a sample of size n from a Normal distribution having known variance σ2 and

unknown mean µ. Compute your estimators if the observed sample is 3, 6, 2, 0, 0, 3.
ii) A pollution study of areas in Delhi found the following amount of PM2.5 (measured

in ppm) in 5 different samples from various areas in Delhi
0.22, 0.27, 0.32, 0.33 and 0.36

Assuming that the population sampled is normal, construct a 90% confidence interval

for the true mean level of PM2.5 in Delhi.

iii) On the average, a certain computer part lasts ten years. The length of time the

computer part lasts is exponentially distributed.
a) What is the probability that a computer part lasts more than 7 years?
b) On the average, how long would five computer parts last if they are used one

after another?
iv)For a given sample size, can we say unequivocally that 99% confidence level is to be

preferred to a 95% level? Why or why not?