7.7.3 Let X₁, Xn be a set of independent random variables with a U(0, 8) distribution, and let T= max (X₁,..., Xn) **** (a) Explain why the cumulative distribution function of Tis F(t) = ()" for 0 s (b) Show that the probability density function of Tis g(t) = ( )" foro < t ≤0. (c) Show that 6= "HT

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7.7.3 Let X₁,..., Xn be a set of independent random variables with a U(0, 8) distribution, and let
T = max (X₁,..., Xn)
(a) Explain why the cumulative distribution function of T'is
F(t) = (-)"
for 0 ≤
(b) Show that the probability density function of Tis
f(t) = (;)"
foro < t < 0.
4
(c) Show that
Â="HT
is an unbiased point estimate of 0
) What is the standard error of
(e) Suppose that n = 10 and that the following data values are obtained:
1.2
6.3
7.3
6.4
3.5
0.2
4
What are the values of ? and the standard error of ô?
4.6
7.1 5.0
1.8
Transcribed Image Text:7.7.3 Let X₁,..., Xn be a set of independent random variables with a U(0, 8) distribution, and let T = max (X₁,..., Xn) (a) Explain why the cumulative distribution function of T'is F(t) = (-)" for 0 ≤ (b) Show that the probability density function of Tis f(t) = (;)" foro < t < 0. 4 (c) Show that Â="HT is an unbiased point estimate of 0 ) What is the standard error of (e) Suppose that n = 10 and that the following data values are obtained: 1.2 6.3 7.3 6.4 3.5 0.2 4 What are the values of ? and the standard error of ô? 4.6 7.1 5.0 1.8
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