I think you are confusing the random variable X and the values
in its domain, x. It's true taht
E(X) = integral xf(x)
but you have to integrate over the real line - it's an integral,
not just an anti-derivative. In this case, you find the anti derivative
(I think using integration by parts) and plug in the end points
of the reals (plus & minus infinity), and the answer is 1/lambda.
hope this helps,
Jeph
carol white wrote:
Hi, How to calculate the mean of the distribution of a random
variable? Take the exponential distribution with the probability
density function f(x)=lambda.exp(-lambda.x) where lambda is a
constant and x is a random variable. The mean of this distribution is
the reciprocal of lambda. If the mean is the expected value of x,
which for a continuous random variable E(x) = Integral (x.f(x))dx,
how could E(x) be the reciprocal of lambda?
Regards,
Carol
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