Probability discrete uniform distribution Need help with pro

Probability discrete uniform distribution. Need help with proper notation.

I need to break this into two separates for example:

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Please let me know if this is correct or if there is a better way. Please offer any additional information you feel may be helpful for setting these up. Thank you.

Solution

Note that

P(2<=x<4) = P(2<=x<=3)

because x = 4 is not included.

Note that

P(between x1 and x2 inclusive) = P(X<=x2) -P(X<=x1-1)

Thus,

P(between 2 and 3 inclusive) = P(x<=3) - P(x<=2-1)

P(between 2 and 3 inclusive) = P(x<=3) - P(x<=1) [ANSWER]

Or in terms of F,

P(between 2 and 3 inclusive) = F(3) - F(1) [ANSWER]