Statistical software packages, such as SAS and MINITAB, are capable of generating random numbers from a uniform distribution. For example, the SAS function RANUNI uses a prime modulus 2³¹ – 1 multiplicative generator with modulus and multiplier 397,204,094 to generate a random variable Y from a uniform distribution on the interval (0, 1). This function can be used to generate a uniform random variable on any interval (a, b), where a and b are constants, using an appropriate transformation.

a. Show that the random variable is uniformly distributed on the interval (0, b).

b. Find a function of Y that will be uniformly distributed on the interval (a, b).