20. Let X1, X2, ..., Xn be independent, Exp(a)-distributed random vari- ables, and set Y = X(1) and Y = X(k)- X(x-1): for 2

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20. Let X1, X2,
ables, and set
X, be independent, Exp(a)-distributed random vari-
Y1 = X(1)
and Y = X(k) – X(k-1);
for 2<k<n.
(a) Show that Y, Y,. Y, are mdependent, and determine their dis-
tributions.
(b) Determine E X(m) and Var Xn)-
Transcribed Image Text:20. Let X1, X2, ables, and set X, be independent, Exp(a)-distributed random vari- Y1 = X(1) and Y = X(k) – X(k-1); for 2<k<n. (a) Show that Y, Y,. Y, are mdependent, and determine their dis- tributions. (b) Determine E X(m) and Var Xn)-
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