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a) If X1...Xn are independent U(0,1) random variables and Y = ( ∏ from i=1 to n of Xi)^1/n, show that nlogY has m.g.f. (1 + z)^-n. i=1 (Hint: first find the m.g.f. of log Xi.
(b) Suppose that Y has density [n^n/(n-1)!](-y log y)^n-1 on (0,1). Show that E(Y^nz) =(1 + z)^-n. (Hint: start by substituting t = -log y.) (Here you may use the fact that integral form 0 to infinity of (s^n-1)ds = (n-1)! for n = 1, 2...)
(c) Deduce that the random variable Y in (a) has the density given in (b).
a souvenir retailer has an opportunity to establish a new location inside a large airport. the annual returns will
Probability using discrete distribution.The probability distribution for the random variable x follows.
according to u.s. news amp world report data in 1995 tuition costs at indiana university a public university were 2984
what is the post-test probability of disease being present in a patient with a positive test result for test A if a cutoff value of 4.0 mg/ml is chosen?
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a recent survey reported that 38 of all students in grades 9 through 12 participate in team sports run by organizations
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Find the critical t alpha/2 assuming the population is normally distributed, the confidence level is 95%, n=101 and sigma is unknown.
a) Let X be the number of teams from IU on Pete's season schedule. What's the probability that none of the Pete's opponents are from IU? What distribution and parameter(s) are you using?
question consider the following two designs for a 28-3 fractional factorial design.design inbsp design
suppose we want to determine the binomial probabilityp of getting 4 heads in 15 flips of a 2-sided coin.nbsp using
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