Can someone solve this and show how?

4. Suppose that the position-dependent wave function of a particle is given by 1 (x-x.) g(x)= e 40 V2TO where x is the position coordinate, Xo is the "peak" position, and ox is the standard deviation in the position coordinate. Confirm that g (x) is normalized over the interval [-co, oo]. 5. Using the wave function g (x) of problem 4, evaluate the integral expression for the mean position (x). 6. Using the wave function g(x) of problems 4 and 5, evaluate the integral expression for the variance of = ((x - x )?), and confirm that your answer makes physical sense. Also, state the value of the standard deviation ox.3. If the average value of t is taken to be 0, the variance of t is given by 1/2 a/2 of = = [ (t - >If (+)12 at = = tz If (t)12 dt. -a/2 - a /2 Determine the variance of by evaluating the above integral, and also state the value of the standard deviation, ot- 4. Suppose that the position-dependent wave function of a particle is given by 1 (x-x0)2 g ( x ) = e 40 V21Ox