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Let X., X 2 , • • • , X11 be a random sample from each of the following distributions involving the parameter 0. In each case find the m.l.e. of 8 and show that it is a sufficient statistic for 8 and hence a minimal sufficient statistic.
(a) b(l , 8), where O 8 J.
(b) Poisson with mean 8 > 0.
(c) Gamma with rt = 3 and p = (} > 0.
(d) N(8, I), where -oo 8 oo.
(e) N(O, 8), where O <>8 oo.
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mean is 100 and sd is 16. doug has an iq of 76. what proportion of people have a higher iq than
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If the proposal textbook receives favorable reviews, how should the editor revise the probabilities of the various outcomes to take this information into account?
Cars arrive at a toll booth at a mean rate of five cars every 10 minutes according to a Poisson process. Find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
A confidence interval increases in width as:
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