True.
This is known as the complementary cumulative distribution function (CCDF) or reliability function, and it represents the probability that X is greater than some threshold t. By integrating this function over all possible values of t, we obtain the expected value of X. This relationship is known as the "tail integral formula" or "survival function formula" for the expected value.
The expected value of a non-negative continuous random variable X, which is defined by
E(X) = ∫ x * fx(x) dx with lower limit 0 and upper limite infinite
also satisfies E(X) = ∫ P(X > t) dt with lower limit 0 and upper limite infinite
True or false?
1 answer