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Math Help - Exponential Distribution

  1. #1
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    Smile 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!!
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  2. #2
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    Quote Originally Posted by Funkz View Post
    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.
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