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Math Help - Normal Distribution problem

  1. #1
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    Normal Distribution problem

    Suppose X and Y are independent random variables with standard Normal Distributions. The probability of X < -1 is some p (from 0,1) . What is the probability of the event:
    X^2 > 1 and Y^3 < -1 ?

    a. 3p
    b. p^2
    c. 2p^2
    d. 3p^2
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  2. #2
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    Quote Originally Posted by champrock View Post
    Suppose X and Y are independent random variables with standard Normal Distributions. The probability of X < -1 is some p (from 0,1) . What is the probability of the event:
    X^2 > 1 and Y^3 < -1 ?

    a. 3p
    b. p^2
    c. 2p^2
    d. 3p^2
    \Pr(X^2 > 1) = \Pr(X < -1) + \Pr(X > 1) = 2p.

    \Pr(Y^3 < -1) = \Pr(Y < -1) = p.

    And if X and Y are independent then X^2 and Y^3 are independent.
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