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6. Suppose an independent sample (X1, X2, X3) is taken from a random variable X having mean p and variance o. Choose the estimator for u which is both unbiased and efficient. O a) (X1/4 + X2 14+ X3/4) O b) (3X,/8 + 3X2/8+ Xg/4) O c) (2X,/8 + 2X2/8 + Xg/2) O d) (X;/8 + X2/8 + 3X3/4)

6. Suppose an independent sample (X1, X2, X3) is taken from a random variable X having mean p and variance o. Choose the estimator for u which is both unbiased and efficient. O a) (X1/4 + X2 14+ X3/4) O b) (3X,/8 + 3X2/8+ Xg/4) O c) (2X,/8 + 2X2/8 + Xg/2) O d) (X;/8 + X2/8 + 3X3/4)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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5. Suppose X-N(0,1) and Q, and Q2 are Chi-Square Random Variables with n, and no degrees of freedom, respectively. Which of the following statements are true? I) Q1/X will have T distribution with n, degrees of freedom II) Q1/n2+Q2/n1 will have a Chi-Square distribution with n + n2 degrees of freedom. III) X2 will have a Chi-Square Distribution with 1 degree of freedom IV) (Q1/n1)/(Q2/n2) will have an F Distribution with n, and n2 degrees of freedom O a) I and III and IV only are true O b) Il and III only are true O c) I and III only are true O d) III and IV only are true 6. Suppose an independent mple (X, X2, Xa} is taken from a random variable X having mean u and variance o. Choose the estimator foru which is both unbiased and efficient. O a) (X1/4 + X2 14+ X3/4) O b) (3X4/8 + 3X2/8+ Xg/4) O c) (2X1/8 + 2X2/8 + X3/2) O d) (X1/8 + X2/8 + 3X3/4)
Transcribed Image Text:5. Suppose X-N(0,1) and Q, and Q2 are Chi-Square Random Variables with n, and no degrees of freedom, respectively. Which of the following statements are true? I) Q1/X will have T distribution with n, degrees of freedom II) Q1/n2+Q2/n1 will have a Chi-Square distribution with n + n2 degrees of freedom. III) X2 will have a Chi-Square Distribution with 1 degree of freedom IV) (Q1/n1)/(Q2/n2) will have an F Distribution with n, and n2 degrees of freedom O a) I and III and IV only are true O b) Il and III only are true O c) I and III only are true O d) III and IV only are true 6. Suppose an independent mple (X, X2, Xa} is taken from a random variable X having mean u and variance o. Choose the estimator foru which is both unbiased and efficient. O a) (X1/4 + X2 14+ X3/4) O b) (3X4/8 + 3X2/8+ Xg/4) O c) (2X1/8 + 2X2/8 + X3/2) O d) (X1/8 + X2/8 + 3X3/4)
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