# Inverse Uniform Distribution Work for a = 3.5, b = 7.2 & P = 0.25

Inverse uniform distribution example problem workout with steps & calculation summary to estimate the random variable x lies between two points a = 3.5 & b = 7.2 for 0.25 probability in statistical experiments.

Calculation Summary
a 3.5
b7.2
P 0.25
x 4.425
mean µ5.35
Median 5.35
variance σ21.1408

## Workout with steps for a = 3.5, b = 7.2 & P = 0.25

Question:
An uniform distribution has the probability of random variable P(x) = 0.25 between the lower limit a = 3.5 and upper limit b = 7.2. What is the inverse probability density function of this distribution to estimate the random variable?
workout :
step 1 Address the input parameter & values
a = 3.5
b = 7.2
P = 0.25

step 2 Find x value using a , b & P values
x = a + (P (b - a))
= 3.5 + (0.25 x (7.2 - 3.5))
= 3.5 + (0.25 x (3.7)
= 3.5 + 0.925
x = 4.425

step 3 Find Mean using a & b values
Mean µ = (a + b)/2
= (3.5 + 7.2)/2
= 10.7/2
Mean µ = 5.35

step 4 Find Median using a & b values
Median =a + b/2
= 3.5 + 7.2/2
= 10.7/2
Median = 5.35

step 5 Find variance using a & b values
Variance σ2 = (b - a)212
= (7.2 - 3.5)212
= (3.7)212
= 13.69/12
Variance σ2 = 1.1408