- #1

- 26

- 0

how could i show something like

[tex]\operatorname{E}(X|X \geq \tau)=\tau+\frac 1 \theta[/tex]

?

i have get the idea of using Memorylessness property here,

but how can i combine the probabilty with the expectation?

thanks.

casper

- Thread starter ghostyc
- Start date

- #1

- 26

- 0

how could i show something like

[tex]\operatorname{E}(X|X \geq \tau)=\tau+\frac 1 \theta[/tex]

?

i have get the idea of using Memorylessness property here,

but how can i combine the probabilty with the expectation?

thanks.

casper

- #2

- 525

- 5

If you write down mathematically the Memorynessless property then it might become obvious. Otherwise it's fine to express the conditional expectation as a ratio of integrals and evaluate it directly.i have get the idea of using Memorylessness property here,

but how can i combine the probabilty with the expectation?

- #3

- 26

- 0

[tex]\Pr(T > s + t\; |\; T > s) = \Pr(T > t) \;\; \hbox{for all}\ s, t \ge 0. [/tex]If you write down mathematically the Memorynessless property then it might become obvious. Otherwise it's fine to express the conditional expectation as a ratio of integrals and evaluate it directly.

i just cant convert from expectation to the probability...

damn

- #4

- #5

- 525

- 5

Hint: rewrite the memoryless property into a form suitable to use on line 1 of your proof. Conditional probabilities -> conditional cdf -> conditional pdf.That's what I did so far.

But I just cant use the memoryless property to do it ....

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