My probability book defines a discrete uniform random variable as a variable X such that P(X=x) = 1/(b-a+1), for all x=a,a+1...b. I was wondering, in a discrete uniform distribution must the numbers that the random variable may take on always be intenger and sequential? And if so, why? I mean, could there be a uniform distribution of the form P(X=x) = 1/4, if x=3,5,6.4,9; and = 0 otherwise? Athough it does make sense to me, (since there are 4 possible outcomes with equal probability, so each individual probability must = 1/4), it doesn't seem tlo fit that definition: 1/(b-a+1) = 1/(9-3+1) is different from 1/4. What am I getting wrong? Thanks.
