# Uniform Distribution Probability for a =2, b = 9 & x = 4

## Workout with steps for a = 2, b = 9 & x = 4

__Question:__

A random variable x has the uniform distribution with the lower limit a = 2 and upper limit b =9. Evaluate the

*probability*of random variable x = 4 which lies between the limits of distribution.

__Workout :__

step 1 Address the formula input parameter & values

a = 2

b = 9

x = 4

step 2 Find P value using a, b & x values

f(x) = 1/b - a

= 1/9 - 2

= 1/7

P = 0.1429

step 3 Find Mean using a & b values

Mean µ = (a + b)/2

= (2 + 9)/2

= 11/2

Mean µ = 5.5

step 4 Find Median using a & b values

Median =a + b/2

= 2 + 9/2

= 11/2

Median = 5.5

step 5 Find variance using a & b values

Variance σ

^{2}= (b - a)

^{2}12

= (9 - 2)

^{2}12

= (7)

^{2}12

= 49/12

Variance σ

^{2}= 4.0833