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Let X1. Xn n independent and identically distributed random variables with common mean u=1 and standard deviation o=2. We let X denote the empirical mean of the sample X1., Xn. v Veuillez choisir au moins une réponse : O a. By the law of large number, X"2 when n- O b. By the law of large number, X1 when n Oc. By the central limit theorem, XN(0,1) O d. By the central limit theorem, X-12/n N(0.1) O e. By the central limit theorem, XN(1,2/n). Of. By the central limit theorem, for any a,b whatever the distribution of X1. Xn, P(as X-12/n sb) P(asZsb) where Z-N(0,1).

Let X1. Xn n independent and identically distributed random variables with common mean u=1 and standard deviation o=2. We let X denote the empirical mean of the sample X1., Xn. v Veuillez choisir au moins une réponse : O a. By the law of large number, X"2 when n- O b. By the law of large number, X1 when n Oc. By the central limit theorem, XN(0,1) O d. By the central limit theorem, X-12/n N(0.1) O e. By the central limit theorem, XN(1,2/n). Of. By the central limit theorem, for any a,b whatever the distribution of X1. Xn, P(as X-12/n sb) P(asZsb) where Z-N(0,1).

Calculus For The Life Sciences
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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
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Let X1 ,.., Xn n independent and identically distributed random variables with common mean u=1 and standard deviation o=2. We let X¯ denote the empirical mean of the sample X1 ..., Xn . Which of the following statements are true? Veuillez choisir au moins une réponse : a. By the law of large number, X¯→2 when n→∞ O b. By the law of large number, X¯→1 when n>0 C. By the central limit theorem, X¯~N(0,1) d. By the central limit theorem, X¯-12/n -N(0,1) e. By the central limit theorem, X¯~N(1,2/n). O f. By the central limit theorem, for any a,b whatever the distribution of X1 .., Xn , P(as X-12/n sb)-P(asZ<b) where Z~N(0,1).
Transcribed Image Text:Let X1 ,.., Xn n independent and identically distributed random variables with common mean u=1 and standard deviation o=2. We let X¯ denote the empirical mean of the sample X1 ..., Xn . Which of the following statements are true? Veuillez choisir au moins une réponse : a. By the law of large number, X¯→2 when n→∞ O b. By the law of large number, X¯→1 when n>0 C. By the central limit theorem, X¯~N(0,1) d. By the central limit theorem, X¯-12/n -N(0,1) e. By the central limit theorem, X¯~N(1,2/n). O f. By the central limit theorem, for any a,b whatever the distribution of X1 .., Xn , P(as X-12/n sb)-P(asZ<b) where Z~N(0,1).
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