# Uniform Distribution Probability for a =5, b = 15 & x = 7

## Workout with steps for a = 5, b = 15 & x = 7

__Question:__

A random variable x = 7 has the uniform distribution with the lower limit a = 5 and upper limit b =15. Find the mean, median and variance of the distribution along with the

*probability*of random variable which lies between the limits?

__Workout :__

step 1 Address the formula input parameter & values

a = 5

b = 15

x = 7

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

f(x) = 1/b - a

= 1/15 - 5

= 1/10

P = 0.1

step 3 Find Mean using a & b values

Mean µ = (a + b)/2

= (5 + 15)/2

= 20/2

Mean µ = 10

step 4 Find Median using a & b values

Median =a + b/2

= 5 + 15/2

= 20/2

Median = 10

step 5 Find variance using a & b values

Variance σ

^{2}= (b - a)

^{2}12

= (15 - 5)

^{2}12

= (10)

^{2}12

= 100/12

Variance σ

^{2}= 8.3333