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Math Help - Conditital probability of a random variable.

  1. #1
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    Conditital probability of a random variable.

    I given that the pdf of a continuous random variable X is

    f(x) = e^{-x} for x > 0 and 0 for x \leq 0

    I have to find P(X \leq 2 | X > 1)<br />
    Am I correct in thinking that

    P((X \leq 2) \cap (X > 1)) = P(1 < X \leq 2) ?
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  2. #2
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    Quote Originally Posted by Sheld View Post
    I given that the pdf of a continuous random variable X is

    f(x) = e^{-x} for x > 0 and 0 for x \leq 0

    I have to find P(X \leq 2 | X > 1)<br />
    Am I correct in thinking that

    P((X \leq 2) \cap (X > 1)) = P(1 < X \leq 2) ?
    Yes.
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  3. #3
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    Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?
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    Quote Originally Posted by Sheld View Post
    Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?
    I think so.
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  5. #5
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Sheld View Post
    Thanks for answer. I have another quick question, when they say find the distribution of a random variable X, they mean the cumulative distribution function, right?
    It can mean either the cumulative or the density.
    In this case I would say, it's an exponential with mean, beta=1.
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