Exam p problem

[Idontunderstand]

The loss due to fire in a commercial building is modeled by a random variable x with a density function f(x) { 0.005(20-x) for 0<x<20 0 otherwise.

Given that a fire loss exceeds 8, what is the probability that it exceeds 16?

The solution shows integrating from x to 20 0.005(20-t) dt.

Can somebody explain why we are not integrating from 0 to 20? Is it because x represents the loss when a fire happens? the only way that we have zero is with no fire.

Why did the "x" get changed to a t? is it because we are integrating with a x and it would be confusing if we did not change to another letter?

 

[srmichael]

The loss due to fire in a commercial building is modeled by a random variable x with a density function f(x) { 0.005(20-x) for 0<x<20 0 otherwise.

Given that a fire loss exceeds 8, what is the probability that it exceeds 16?

The solution shows integrating from x to 20 0.005(20-t) dt.

Can somebody explain why we are not integrating from 0 to 20? Is it because x represents the loss when a fire happens? the only way that we have zero is with no fire.

Why did the "x" get changed to a t? is it because we are integrating with a x and it would be confusing if we did not change to another letter?

By definition, \(\displaystyle P(X>x)=\int^{20}_x 0.005(20-t)dt\). This will get us a formula for the CDF of this function. Then you can use the definition of conditional probability: \(\displaystyle P(A|B)=\dfrac{P(A \cap B)}{P(B)}\).

Give it a shot and let us know if you get stuck.