Let X1, X2,., Xn be a random sample from a uniform distribution on the interval [0, 0] , so that f(x) = 1/0 if 0 s x


Let X1, X2,., Xn be a random sample from a uniform distribution on the interval [0, 0] , so that<br>f(x) = 1/0<br>if 0 s x< 0<br>Then if Y = max (X), it can be shown that the random variable U = Y/0 has density function<br>f(u) = nun-1<br>if 0 sus1<br>If<br>P( (a/2)1/n < Y/0 < (1-a/2)/n)=1-a<br>а.<br>Derive a 100(1-a)% Cl for 0 based on this probability statement.<br>If my waiting time for a morning bus is uniformly distributed and observed waiting times are x,=4.2, x2=3.5, X3=1.7 ,X4=1.2 , and x5=2.4, (Use 3<br>digits after decimal point)<br>95% CI for 0 is [<br>b. If<br>P( a/n < Y/0 < 1)=1-a<br>Derive a 100(1-a)% CI for 0 based on this probability statement.<br>If my waiting time for a morning bus is uniformly distributed and observed waiting times are x1=4.2, x2=3.5, X3=1.7 ,X4=1.2 , and x5=2.4, (Use 3<br>digits after decimal point)<br>95% CI for 0 is [<br>Which of the two intervals derived previously is shorter?<br>C.<br>

Extracted text: Let X1, X2,., Xn be a random sample from a uniform distribution on the interval [0, 0] , so that f(x) = 1/0 if 0 s x< 0="" then="" if="" y="max" (x),="" it="" can="" be="" shown="" that="" the="" random="" variable="" u="Y/0" has="" density="" function="" f(u)="nun-1" if="" 0="" sus1="" if="" p(="" (a/2)1/n="">< y/0="">< (1-a/2)/n)="1-a" а.="" derive="" a="" 100(1-a)%="" cl="" for="" 0="" based="" on="" this="" probability="" statement.="" if="" my="" waiting="" time="" for="" a="" morning="" bus="" is="" uniformly="" distributed="" and="" observed="" waiting="" times="" are="" x,="4.2," x2="3.5," x3="1.7" ,x4="1.2" ,="" and="" x5="2.4," (use="" 3="" digits="" after="" decimal="" point)="" 95%="" ci="" for="" 0="" is="" [="" b.="" if="" p(="" a/n="">< y/0="">< 1)="1-a" derive="" a="" 100(1-a)%="" ci="" for="" 0="" based="" on="" this="" probability="" statement.="" if="" my="" waiting="" time="" for="" a="" morning="" bus="" is="" uniformly="" distributed="" and="" observed="" waiting="" times="" are="" x1="4.2," x2="3.5," x3="1.7" ,x4="1.2" ,="" and="" x5="2.4," (use="" 3="" digits="" after="" decimal="" point)="" 95%="" ci="" for="" 0="" is="" [="" which="" of="" the="" two="" intervals="" derived="" previously="" is="" shorter?="">

Jun 09, 2022
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