Independent solution

How to solve this Uniform Distribution question

Setup

Setup

Intersect the failure event with the information that the lifetime has already exceeded a.

Pr⁡(T<30∣T>a)=Pr⁡(a<T<30)Pr⁡(T>a)\Pr(T<30\mid T>a)=\frac{\Pr(a<T<30)}{\Pr(T>a)}

Model

Model

For a uniform lifetime, these probabilities are proportional to interval lengths.

Pr⁡(T<30∣T>a)=30−a40−a\Pr(T<30\mid T>a)=\frac{30-a}{40-a}

Compute

Compute

Set the conditional interval ratio to the supplied probability and solve.

30−a40−a=0.60\frac{30-a}{40-a}=0.60
30−a=24−0.60a30-a=24-0.60a
a=15a=15

Answer

Answer

The conditioning age is 15 months.

15(C)\boxed{15\quad\text{(C)}}