# Uniform Distribution Probability for a =5, b = 15 & x = 7 Uniform distribution example problem workout with steps & calculation summary for the probabilty of random variable x = 7 lies between two points a = 5 & b = 15 in statistical experiments.

Calculation Summary
a 5
b15
x7
P 0.1
mean µ10
Median 10
variance σ28.3333

## 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 σ2 = (b - a)212
= (15 - 5)212
= (10)212
= 100/12
Variance σ2 = 8.3333 