Let X be a random variable with (continuous) distribution function F. Let m = q0.5 = Finv(0.5) be the median of F and define the random variable c. Use b to conclude that the MAD of an N(µ, σ2)...

Let X be a random variable with (continuous) distribution function F. Let m = q0.5 = Finv(0.5) be the median of F and define the random variable

c. Use b to conclude that the MAD of an N(µ, σ2) distribution is equal to σΦinv(3/4), where Φ is the distribution function of a standard normal distribution. Recall that the distribution function F of an N(µ, σ2) can be written as