Thread: E[x^(-1/2)] of exponential distribution

have a hard time to calculate the expected value below
E[x^(-1/2)], x is an exponential distribution of beta. I tried to transformed to a gamma but not succeed. the interal is way too big for me figure out. Thanks.

Originally Posted by MJM

have a hard time to calculate the expected value below
E[x^(-1/2)], x is an exponential distribution of beta. I tried to transformed to a gamma but not succeed. the interal is way too big for me figure out. Thanks.

You need to compute . You should try to substitute ; it will give you an integral involving the Gaussian density function. From there you can conclude.

Thanks. It works nicely.