2.10.1 Continuous Uniform

Question 1

What is a continuous uniform distribution?

Answer 1

A probability distribution where every interval of the same length within the domain is equally likely to occur.

f(x) =1/(b-a), from a to b inclusive

Question 2

What does the PDF of the continuous uniform tell us about the likelihood of different values?

Answer 2

Since the PDF is a constant, every value in the range has the same likelihood, meaning it is equally likely to occur.

Question 3

What is the cumulative distribution function (CDF) of a continuous uniform random variable?

Answer 3

Question 4

What is the mean (expected value) of a continuous uniform distribution?

Answer 4

The midpoint of the interval:
[ E[X] = \frac{a + b}{2} ]

Question 5

What is the variance of a continuous uniform distribution?

Answer 5

The formula for variance is:
[ \text{Var}(X) = \frac{(b - a)^2}{12} ]

Question 6

what are the special relationships for the cont. uniform with a<c<d<b?

Answer 6