Suppose that that a set of observations r1, 22, . ", follow the Rayleigh distribution, i.e. t exp(), r> 0 fx.(x:) = otherwise, for all i e {1, ., n}. You would like to learn the parameter b using the data. .....

D.P(8 150) =

Use what you know about order statistics to show that for the random sample of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ − 1/2 and β = θ + 1/2.

6. The resting pulse rate, X, for a particular population of adult women is normally distributed w mean of 74 beats per minute (bpm) and a standard deviation of 6 bpm. a) Find P(66 s X s 78) b) Find the 60th percentile of women's resting heart rates. c) If a sample of four women is randomly selected, find P(X > 79). d) Suppose now that the sample size is greater than four. Will the probability P(X > 79) be greater than, less than or the same as the value found in part c)? Explain.