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Suppose that a scientist desires to estimate the proportion? of monarch butterflies with a special type of marking on their wings. Suppose he captures monarch butterflies one at a time, and at the end of the day the scientist had captured 60 monarch butterflies and had found only two with special marking.
(a) Show that the family of beta-distributions constitutes a conjugate prior family for this model
(b) Based on some prior research one assumes a beta-prior for ? with parameters a = 1 and b = 9. What is the Bayes estimator of p with respect to quadratic loss?
(c) What is the MLE of ??
Policyholders of a certain insurance company have accidents at times distributed according to a Poisson process with rate λ. The amount of time from when the accident occurs until a claim is made has distribution G.
Suppose we generate a random variable X in the following way. First we ?ip a fair coin. If the coin is heads, take X to have a Unif(0,1) distribution. If the coin is tails, take X to have a Unif(3,4) distribution.
assume that in a population of interest the ratio of males to females is 11. if you choose a random sample of 25 from
A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 67%.
Find the probability that the test for a pooled sample of k people will be positive - what is the expected value of the number X of tests necessary under plan
what is the probability that in the sample fewer than 35 are willing to spend extra for products and services from
The sample of 200 voters and tests Ho: P=0.5 versus H1:P(not equal)0.5 at 5% level. What is the power of the test if the true value of P is 0.55?
Let Y, Y2 denote the order statistics of a random sample of size 2 from a distribution which is N(µ, u2), where u2 is known.(a) Show that Pr ( Y1 µ Y2 ) = !and compute the expected value of the random length Y2 - Y, .
Let ρk = λk/μk and ρ = ρ1+ρ2+·· ·+ρK . In particular, show, as before, that the probability of n customers in the system is Qn = p(0, ... , 0)ρn/n! for 0 ≤ n ≤ m.
explain the difference between a left-tailed two-tailed and right-tailed test to include when would we choose each type
Dr Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different than the historical grade distribution. Use a =.05 and .01 and perform a goodness of fit test.
1. An experiment has four possible outcomes A, B, C, and D. Check whether the following assignments of probability are possible:
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