Let X be a random variable with cumulative distribution func

Let X be a random variable with cumulative distribution function Is X a discrete or continuous random variable? Explain clearly in terms of the property of a discrete or continuous random variable.

Solution

If a variable is defined at specific values and it cannot take values between the values then it will be discrete random variable. Given CDF is defined at 0.1, 0.2, 0.3 and 0.4 and not in between values. So it is discrete distribution.