Final answer:
To compute the given integral, we can use the properties of the normal distribution and rewrite it in terms of the cumulative distribution function. However, since the integral does not have a simple closed form solution, it needs to be evaluated numerically using special methods or software.
Step-by-step explanation:
To compute the integral ∫[infinity]−[infinity]Φ(x)[1−Φ(x−μσ)]dx, we can use the properties of the normal distribution. Φ(x) represents the cumulative distribution function (CDF) of a standard normal distribution, which gives the probability that a random variable is less than or equal to a given value. We can rewrite the integral as ∫[infinity]−[infinity]Φ(x) - Φ(x-μσ)dx.
For simplicity, let's define a new function G(x) = Φ(x) - Φ(x-μσ). Now, we can integrate G(x) over the whole real line. However, since the cumulative distribution function is not expressible in terms of elementary functions, the integral does not have a simple closed form solution and needs to be evaluated numerically using special methods or software.