6 10 11 12 Suppose that Yl Y21 quot Yn denote a random sample of size n from a Poisson distribution with mean A Consider A1 Y1 Yg 2 and
Suppose that Yl Y quot Yn denote a random sample of size n from a Poisson distribution with mean A
Suppose that Yl Y quot Yn denote a random sample of size n from a
Yn denote a random sample of size n from a Poisson distribution with mean A Consider A Y Yg and
Suppose that Yl Y quot Yn denote a random sample of size n
from a Poisson distribution with mean A Consider A Y Yg and
Suppose that Yl Y quot Yn denote a random sample
Suppose that Yl Y quot
6. 10. 11. 12. Suppose that Yl, Y21'" ,Yn denote a random sample of size n from a Poisson distribution with mean A. Consider A1: (Y1 + Yg)/2 and...

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Thanks for helping me solve these 6 questions these 6 quetions ATTACHMENT PREVIEW Download attachment ???? 2017-08-21 ??1.11.15.png 6. 10. 11. 12. Suppose that Yl, Y21'” ,Yn denote a random sample of size n from a Poisson distribution with mean A. Consider A1: (Y1 + Yg)/2 and A2: Y. Derive the ef?ciency of A1 relative to A2. Which is a better estimate? Why? The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (19,19 + 1), where 6‘ is the true but unknown voltage of the circuit. Suppose that Yl, Y2, ..., Yn denote a random sample of such readings. (a) Show that Y is a biased estimator of 9 and compute the bias. (b) Find a function of Y that is an unbiased estimator of 6'. (c) Find MSE(Y) when Y is used as an estimator of 9. . Let Y1,Y2,. . . ,Yn denote a random sample of size n from an exponential distribution with density function given by, 1 fy(s)= -e_y/9, y > 0- (a) Show that 91 = iii/(1) is an unbiased estimator for s and ?nd MSE((§1). Hint: What is the distribution of YO)? (b) Show that 52 = Y is an unbiased estimator for 6 and ?nd MSE(§2). (c) Find the ef?ciency of 91 relative to 032. Which estimate is ”better” (i.e., more ef?cient)? . If Y has a binomial distribution with n trials and success probability 3;, show that Y/n is a consistent estimator of p. Let 171,172,. . . ,Yn denote a random sample from the probability density function: 1'14?!) = 9y9_111{0<y<1}i where 9 > 0. Show that Y 1s a consistent estimator of 3 +1 Let Y1,Y2, ...,Yn, denote a random sample from pdf given by (393) e’yZ/g, y > 0 0, otherwise f(y|9) ={ with parameter 0. Show that 2:1 YE is suf?cient for 9. Let Y1, Y2, . . . ,Yn denote a random sample from the probability density function f(y|9) = «rs—'5'). y 2 9. Show that Y0) = min<[Y1, . . . ,Yn} is su?icient for 9. Hint: use an indicator function since the suppmr't depends on 9

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