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.
i) Derive method of moments and maximum-likelihood estimators for parameter µ
based on a sample of size n from a
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?
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