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Let X1, X2,... be i.i.d. random variables each with mean u and variance o2 < 00. Consider the Xn- sequence of random variables Y, Let X, denote the sample mean of X1,...,Xn- From the statements below, select those that are true in general, not just in some special cases. O a. At each fixed point y E R, the cdf of Y, evaluated at y approximately equals the standard normal cdf at that point, (y), with the approximation improving as n increases. O b. Y, has expected value approximately but not necessarily exactly equal to zero. The approximation improves as n increases. O c. X, has expected value approximately but necessarily exactly equal to u. The approximation improves as m increases. O d. Y, has variance equal to one for all n2 1. e. Xn has variance equal to one for all n >1.

Let X1, X2,... be i.i.d. random variables each with mean u and variance o2 < 00. Consider the Xn- sequence of random variables Y, Let X, denote the sample mean of X1,...,Xn- From the statements below, select those that are true in general, not just in some special cases. O a. At each fixed point y E R, the cdf of Y, evaluated at y approximately equals the standard normal cdf at that point, (y), with the approximation improving as n increases. O b. Y, has expected value approximately but not necessarily exactly equal to zero. The approximation improves as n increases. O c. X, has expected value approximately but necessarily exactly equal to u. The approximation improves as m increases. O d. Y, has variance equal to one for all n2 1. e. Xn has variance equal to one for all n >1.

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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Let X1, X2,... be i.i.d. random variables each with mean u and variance o² <0o. Consider the sequence of random variables Y An ..,Xn. From the Xn-p Let Xn denote the sample mean of X1,. statements below, select those that are true in general, not just in some special cases. O a. At each fixed point y E IR, the cdf of Y, evaluated at y approximately equals the standard normal cdf at that point, (y), with the approximation improving as n increases. O b. Y, has expected value approximately but not necessarily exactly equal to zero. The approximation improves as m increases. O c. X, has expected value approximately but necessarily exactly equal to µ. The approximation improves as n increases. d. Y, has variance equal to one for all n >1. e. X, has variance equal to one for alln>1.
Transcribed Image Text:Let X1, X2,... be i.i.d. random variables each with mean u and variance o² <0o. Consider the sequence of random variables Y An ..,Xn. From the Xn-p Let Xn denote the sample mean of X1,. statements below, select those that are true in general, not just in some special cases. O a. At each fixed point y E IR, the cdf of Y, evaluated at y approximately equals the standard normal cdf at that point, (y), with the approximation improving as n increases. O b. Y, has expected value approximately but not necessarily exactly equal to zero. The approximation improves as m increases. O c. X, has expected value approximately but necessarily exactly equal to µ. The approximation improves as n increases. d. Y, has variance equal to one for all n >1. e. X, has variance equal to one for alln>1.
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