Let X be an exponential random variable with parameter λ. Show that the conditional expectation of X given X > t is equal to the expectation of X + t for any positive real number t
Added by Katherine P.
Step 1
Now, we want to find the conditional expectation E[X | X > t]. To do this, we need to find the conditional pdf of X given X > t. Using the definition of conditional probability, we have: f(x | X > t) = f(x, X > t) / P(X > t) = f(x) / P(X > t), for x > t. Since Show more…
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