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You've seen an example of a Discrete Uniform Distribution before: rolling a 6-sided dice. This idea can be extended to an 𝑛 -sided dice. No matter how many sides the dice has, with a fair dice, you'd be equally likely to roll every side.

If 𝑎 is the smallest number and 𝑏 is the biggest number that can be observed (for a fair dice, 𝑎=1 , 𝑏=6 )

should be

You've seen an example of a Discrete Uniform Distribution before: rolling a 6-sided die. This idea can be extended to an 𝑛 -sided die. No matter how many sides the die has, with a fair die, you'd be equally likely to roll every side.

If 𝑎 is the smallest number and 𝑏 is the biggest number that can be observed (for a fair die, 𝑎=1 , 𝑏=6 )

in The Discrete Uniform Distribution section:

$$Var(X) = \sqrt{\frac{(b-a)(b-a+2)}{12}}$$

should be

$$Var(X) = \frac{(b-a)(b-a+2)}{12}$$