74. Let X1, X2, ... be a sequence of independent identically distributed contin- uous random variables....

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Answer 1

Answer #1

The following images contain the complete solution :

image 1:

( are ind Now since Xos & continuous & PLX, LX, L-.2x ) - P(x, LX, L.- 2X LX – е х у, 2 - - X, < x ) all in nl cases x, x pe

image 2:

. E P (X; L...2X ) - 1 a permutation & as these are equal to each all of other. t & ( l ., in): a permutation of 1,2,-, n Now

image 3:

record occurs at. 6 let Y:-/ l ,if necond occo l o othenwise, Then number of decounds by time n. ECY) = Ê E(;) since , & ( 4;

image 4:

van (Y) = E CY:) - (CY:)) 1x P(Y; -1) - 12 isi (iv) E(N) = { n. P(Nan) P (N=n) = P( record at time n& no second at time 23,.

image 5:

in 72 P/Nan) = NOV Now, I(N) - Now, E(N) = Emol non-1 n(n-1) [ n=2 1 n-1 2 which is a Harmonic series with p= 7 & we know it

Cheers :)

Answer 2

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