# 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.

## 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 σ

^{2}= (b - a)

^{2}12

= (7.2 - 3.5)

^{2}12

= (3.7)

^{2}12

= 13.69/12

Variance σ

^{2}= 1.1408