Suppose a RV X has a continuous uniform distribution on 0

Suppose a R.V. X has a continuous uniform

distribution on 0<x<5. Find the mean and variance of X. Also find p(4<x<6)

Solution

a)

For uniform disitrbution on (a,b),

Mean = (a+b)/2 = (0+5)/2 = 2.5 [ANSWER, MEAN]

.....

Also,

Variance = (b-a)^2/12 = (5-0)^2/12 = 25/12 or 2.083333333 [ANSWER]

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c)

As the distribution is only up to x = 5,

P(4<x<6) = P(4<x<5)

Thus,

P(4<x<6) = (5-4)/(5-0) = 0.20 [ANSWER]