Problem 2; chapter 8; # 46 Find the sampling distributions of Y1 and Yfor random samples of size n from a continuous uniform population with a =and B 110Problem 3; chapter 8; # 48 Find the mean and the variance of the sam-pling distribution of Y1 for random samples of size n from problem 2 (previousproblem) 22adtY isdf of frst order stahishic-1गरी- पु) ।Ondara otheruisefyy)910दवThe pdf ofE the maximam order stahshcThe taeistmn- na= नगजकगो ।-५oJतहसी दि 0।yफी)ण21 63 atboAYa isorder stanshcpdf of the nth1-1एालि)युलो 3प. S/-otherwiseYnnim1

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Asked Oct 1, 2019
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distributions of both Y1 and Yn are uniform and continuous 

Problem 2; chapter 8; # 46 Find the sampling distributions of Y1 and Y
for random samples of size n from a continuous uniform population with a =
and B 1
10
Problem 3; chapter 8; # 48 Find the mean and the variance of the sam-
pling distribution of Y1 for random samples of size n from problem 2 (previous
problem)
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Problem 2; chapter 8; # 46 Find the sampling distributions of Y1 and Y for random samples of size n from a continuous uniform population with a = and B 1 10 Problem 3; chapter 8; # 48 Find the mean and the variance of the sam- pling distribution of Y1 for random samples of size n from problem 2 (previous problem)

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22
adt
Y is
df of frst order stahishic
-1
गरी- पु) ।
Ondara otheruise
fyy)
910
दव
The pdf ofE the maximam order stahshc
The tae
istm
n- n
a= नगजकगो ।-५oJ
तहसी दि 0।
y
फी)ण
21 63 atboA
Ya is
order stanshc
pdf of the nth
1-1
एालि)
युलो 3प. S/-
otherwise
Yn
nim
1
help_outline

Image Transcriptionclose

22 adt Y is df of frst order stahishic -1 गरी- पु) । Ondara otheruise fyy) 910 दव The pdf ofE the maximam order stahshc The tae istm n- n a= नगजकगो ।-५oJ तहसी दि 0। y फी)ण 21 63 atboA Ya is order stanshc pdf of the nth 1-1 एालि) युलो 3प. S/- otherwise Yn nim 1

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Expert Answer

Step 1

We know that first order statistic PDF is given by fy1(y1) as shown below. 

Mean or Expected value can be calculated using the intergral function used for continuous random variables (also shown below)

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when 0 y otherwise Mean or Expected value E[y,]= | y, f (y,) cdy 0 =5y, n-ydy

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Step 2

This integration can be performed using integration by parts method as shown below.

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Integration by parts:uv' =uv - [ vu* u yi and v'= (1 - y)"1 Integrate v' in first term and take derivative of u in second term y(1y -1-ydy ynyd, =n п п Perform Integration in second term y(y(y,) n+1 = n n(n1 п Compute boundaries for y from 0 to 1 1 n[0 n(n) 1 п+1

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Step 3

Mean is given as...

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1 Mean or Expected value E[y,= | y,f (y)cdy n1 0

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