4.11 (Examination question, St. Andrews University.) The random variable X has the inverse Gaussian distribution, with pdf:

f(x) =  λ

2πx3

1 2

exp 

−λ

2

 x

μ2 − 2

μ

+

1 x

 , 0 ≤ x < ∞, with λ > 0, μ> 0.

For the case of fixed λ, show, by calculating the first-order derivative of