Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Use the supplied exponential standard deviation as its mean scale beta.

β=1000\beta=1000
S(x)=e−x/1000S(x)=e^{-x/1000}

Model

Model

Both thresholds are nested, so divide their survival probabilities or apply the exponential lack-of-memory property.

Pr⁡(X>1500∣X>1000)=S(1500)S(1000)\Pr(X>1500\mid X>1000)=\frac{S(1500)}{S(1000)}
=S(500)=S(500)

Compute

Compute

Evaluate the survival probability for the additional 500 units.

S(500)=e−500/1000=e−0.5=0.6065306597S(500)=e^{-500/1000}=e^{-0.5}=0.6065306597

Answer

Answer

The conditional probability rounds to 0.61.

0.61(D)\boxed{0.61\quad\text{(D)}}