Let be a sequence of independent identically distributes continous random variables. A record occurs at time j ( ) if .

Show that:

[number of records]=

[number of records]=

Thank you very much in advance!

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- Nov 25th 2011, 10:30 AMzadirNumber of records (expected value, variance)
Let be a sequence of independent identically distributes continous random variables. A record occurs at time j ( ) if .

Show that:

[number of records]=

[number of records]=

Thank you very much in advance! - Nov 27th 2011, 10:11 AMdougRe: Number of records (expected value, variance)
First af all, you should calculate:

a) P(X_n is a record)=?

then:

b) E [number of records by time n]=?

c) Var [number of records by time n]=?

I give you some hints how to solve these problems:

For part (a) use symmetry and observe that P(X_i = X_j ) = 0

since X_i’s are continuous random variables. For parts (b) and (c) introduce indicator random variables. Note that these indicator random variables are independent

in this case.

I hope I helped you. :) - Nov 27th 2011, 10:19 AMzadirRe: Number of records (expected value, variance)
Thank you for your help!

On the other hand, to tell the truth, I still can't solve the problem.

I would really appreciate any help!