1) Let X₁, X2,...,X20 be a random sample from a population X with densityf (x; 0) = {(otherwisex 0,1.where 0 < 0≤is a parameter. The hypothesis Ho: to be tested againstH₁:p?

X~Ber(θ) Farmula used nCr=r!/(n!(n-r)!) r!=r(r-1)x..3×2×1

Answered: {0*(1- (ex (1-0)¹-x, x = 0,1. 0,…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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13. Let Y,, Y2, ..., Yn denote a random sample from a population with pdf f(yl0) = (0 + 1)yº,0 -1 a) Find an estimator for theta by the method of moments. b) Find the maximum likelihood estimator for theta.
If X₁, X2,..., Xn constitute a random sample of size n from an exponential population, show that X is a sufficient estimator of the parameter 0.
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The proportion of students who get an undergraduate degree in statistics in four years was compared for meals and females. Random sample of 200 male statistics majors and 200 female statistics majors were taken. Choose the appropriate parameter(s) for this situation. [Hint: The .parameter(s) to be used in your hypothesis] ule u 2.00 jo None of these .A O P1-P2.B O H.C O Hi- H2.D O P.E O إنهاء المحاولة . . . PREVIOUS ACTIVITY Note P Type here to search Ae Ps 近

B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parameters unknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e. s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean]. %3D n-1 Li%3D1 [Hint: a2 (п-1)52 -~x~-1 which has mean (n-1) and variance 2(n-1)] i) Show that S2 is unbiased for o2. Find variance of S2. ii) Find the bias of 62 and the variance of ô2. iii) Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?. iv) Show that both S2 and ô? are consistent estimators for o?.
EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0

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{0*(1- (ex (1-0)¹-x, x = 0,1. 0, otherwise where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against H₁: p=