Question

Suppose X is a uniform random variable on the interval (0, 1). Find the range and the distribution and density functions of Y = Xn for n ≥ 2.

Answer 1

CUMULATIVE DISTRIBUTION:

The cumulative distribution function of a real-valued random variable \ is the function given by^:

{P} (X x)}

(Eq.1)

where the right-hand side represents the probability that the random variable takes on a value less than or equal to }. The probability that l lies in the semi-closed interval , where , is therefore

(Eq.2)

DENSITY FUNCTION: probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.