Discrete uniform distributions
Compute probabilities and expected value for a discrete uniform random variable. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
A fair 6-sided die (faces numbered 1 to 6) is rolled once. Each face is equally likely. What is the probability that the result is between 1 and 4, inclusive?
Answer: 2/3
See one solved, step by step
A discrete random variable X is equally likely to take any integer value from 8 to 13 (inclusive). Find E(X), the expected value of X.
E(X) = (a + b) / 2
📘 Worked solution
1For a discrete uniform distribution over integers a to b, E(X) = (a + b)/2.Every value is equally likely, so the mean is the midpoint of the range.
2E(X) = (8 + 13)/2 = 10.5Add the smallest and largest values and divide by 2.
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