Let X1, X2, ..., Xn be a random sample from a population r.v. X, with range Rx C [a, b]. Furthermore, suppose the mean and variance of X are unknown. Assume that n is large enough. (b – a)? (a) Show that Var(X) <

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Let X1, X2, ..., X, be a random sample from a population r.v. X, with range Rx c
[a, b]. Furthermore, suppose the mean and variance of X are unknown. Assume that n
is large enough.
(b – a)?
(a) Show that Var(X) <
b – a
(b) Let a € (0, 1). Show that (X- 24 2n
b
a
where (ze) = 1-
is a confidence interval for E[X] with (1 – a)100% confidence level.
Transcribed Image Text:Let X1, X2, ..., X, be a random sample from a population r.v. X, with range Rx c [a, b]. Furthermore, suppose the mean and variance of X are unknown. Assume that n is large enough. (b – a)? (a) Show that Var(X) < b – a (b) Let a € (0, 1). Show that (X- 24 2n b a where (ze) = 1- is a confidence interval for E[X] with (1 – a)100% confidence level.
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