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

Uniform distribution example problem workout with steps & calculation summary for the probabilty of random variable x = 4 lies between two points a = 2 & b = 9 in statistical experiments.

Calculation Summary
a 2
b9
x4
P 0.1429
mean µ5.5
Median 5.5
variance σ24.0833

## 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 σ2 = (b - a)212
= (9 - 2)212
= (7)212
= 49/12
Variance σ2 = 4.0833