Suppose X = Exp(1) and Y= -ln(x)
(a)Find the cumulative distribution function of Y .
(b) Find the probability density function of Y .
(c) Let X1, X2, ... , Xk be i.i.d. Exp(1), and let Mk = max{X1,..... , Xk)(Maximum of X1, ..., Xk). Find the probability density function of Mk.(Hint: P(min(X1, X2, X3) > k) = P(X1 >= k, X2 >= k, X3 >= kq, how about max ?)
Solution,
a)
cdf of Y :
,
b)
pdf of Y :
c)
cdf of Mx :
pdf of Mk : d)
cdf of Z :
= FY(z) [ a = -e-z
the hint]
Suppose X = Exp(1) and Y= -ln(x) (a)Find the cumulative distribution function of Y . (b)...
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