Continuous uniform distribution

Question 1

What is a continuous uniform distribution?

Answer 1

A distribution in which every interval of equal width within the range of the parameters is equally likely

Question 2

How is a continuous uniform distribution notated?

Answer 2

X∼U(a,b)

Question 3

What is the probability density function of a random variable X∼U(a,b)

Answer 3

f(x)={1/(b-a) for a≤x≤b, 0 otherwise}

Question 4

For a random variable X∼U(a,b), how can E(X) be calculated?

Answer 4

(a+b)/2

Question 5

For a random variable X∼U(a,b), how can Var(X) be calculated?

Answer 5

(b-a)²/12

Question 6

For a random variable X∼U(a,b), what is its cumulative distribution function F?

Answer 6

F(x)={0 for x<a, (x-a)/(b-a) for a≤x≤b, 1 for x>b}