Let the pmf of X be defined by fx 62x2 x 123 Show that EX

Let the pmf of X be defined by f(x) = 6/(2x2), x = 1,2,3,.... Show that E(X) = + and thus, does not exist.

Solution

Given that the p.m.f. of X is

f(x) = 6 / ²x² , x=1,2,3,......

The expected of X is given by,

E(X) =   x * f(x) dx (x is from 1 to )

=  x * 6 / ²x² dx     (x is from 1 to )

= 6 / ² x / x² dx     (x is from 1 to )

= 6 / ²  1/x dx     (x is from 1 to )

= 6 / ² () =

E(X) =