# Math Help - Exponential Distribution

1. ## Exponential Distribution

Hi, can someone guide me on how to solve a question related to exponential distribution? Thanks in advance!

An exponential random variable X has its pdf given by
f (x;λ) = λexp{−λx} for x ≥ 0
The value of λ is not given

Q:Compute P(k < X ≤ k + 1) for k = 0, 1, . . ..

P(k < X ≤ k + 1) = F(k+1) - F(k)
Do I use CDF? Which would just be

= exp(-λk)-exp(-λ(k+1))

= exp(-λk)(1-exp(-λ))

Is there more step to it? I am assuming I need some sort of value.

Thanks again!!

2. Originally Posted by Funkz
Hi, can someone guide me on how to solve a question related to exponential distribution? Thanks in advance!

An exponential random variable X has its pdf given by
f (x;λ) = λexp{−λx} for x ≥ 0
The value of λ is not given

Q:Compute P(k < X ≤ k + 1) for k = 0, 1, . . ..

P(k < X ≤ k + 1) = F(k+1) - F(k)
Do I use CDF? Which would just be

= exp(-λk)-exp(-λ(k+1))

= exp(-λk)(1-exp(-λ))

Is there more step to it? I am assuming I need some sort of value.

Thanks again!!
The answer is simply $\displaystyle \int_{k}^{k+1} \lambda e^{-\lambda x}\, dx$ and obviously will depend on k.