A random variable follows a continuous uniform distribution

A random variable follows a continuous uniform distribution between 15 and 45.

A. What is the mean of this distribution?

B. What is the standard deviation of this distribution?

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

f(x) = 1/(b-a) = 1 / (45-15) = 1 / 30 = 0.0333
a)
Mean = a + b / 2 = 30
b)
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 8.66

c)
P(X > 25) = (45-25) * f(x)
= 20*0.0333
= 0.666

P(X <= 25) = 1 - P(X > 25) = 1 - 0.666 = 0.334