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Math Help - find cumulative distribution function

  1. #1
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    find cumulative distribution function

    plz solve this problem in detail
    Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of cumulative distribution function F(X) at x=-1 and +1 are....?

    (A) 0 and 0.5 (B) 0 and 1 (C) 0.5 and 1 (D) 0.25 and 0.75
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  2. #2
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    Re: find cumulative distribution function

    Hey balajikcp8.

    Hint: The CDF is denoted by P(X <= x) (What can you say about P(X <= -1) and P(X <= +1))?
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  3. #3
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    Re: find cumulative distribution function

    P(X <= +1)=1. but P(X <= -1)...?
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  4. #4
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    Re: find cumulative distribution function

    Hint: Including the value -1 (as opposed to not) includes the probability of that observation.
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  5. #5
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    Re: find cumulative distribution function

    sorry i can't understand. if possible pls explain
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  6. #6
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    Re: find cumulative distribution function

    Basically P(X <= -1) is the probability that X takes on a value of -1 or anything below -1.

    We know that P(X = -1) = 0.5 and P(X <= -1) = P(X < -1) + P(X = -1).

    Now P(X = -1) = 0.5 but P(X < -1) = 0 which means P(X <= -1) = 0 + 0.5 = 0.5
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  7. #7
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    Re: find cumulative distribution function

    Thanks a lot
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