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Math Help - Independent standard normal variables

  1. #1
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    Independent standard normal variables

    Let X and Y be independent standard normal variables. Find:
    a) P(3X + 2Y > 5)
    b) P(min(X,Y) < 1)
    c) P(|min(X,Y)| < 1)
    d) P(min(X,Y) > max(X,Y) - 1)

    I know this is probably pretty straight forward, but I'm not sure how to do these ... I know, for example, part a is N(0,13) , but how do you know what to look up in the table? Thanks!
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  2. #2
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    Quote Originally Posted by tbl9301 View Post
    Let X and Y be independent standard normal variables. Find:
    a) P(3X + 2Y > 5)
    b) P(min(X,Y) < 1)
    c) P(|min(X,Y)| < 1)
    d) P(min(X,Y) > max(X,Y) - 1)

    I know this is probably pretty straight forward, but I'm not sure how to do these ... I know, for example, part a is N(0,13) , but how do you know what to look up in the table? Thanks!
    You're expected to know that if X and Y are independent and X ~ Normal (\mu_1, \sigma^2_1)and Y ~ Normal (\mu_2, \sigma^2_2) then U = aX + bY ~ Normal (\mu = a \mu_1 + b \mu_2, \sigma^2 = a^2 \sigma^2_1 + b^2 \sigma_2^2).
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  3. #3
    MHF Contributor matheagle's Avatar
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    P(min(X,Y) < 1)=1-P(min(X,Y) > 1)=1-P(X>1,Y>1)=1-P(X>1)P(Y>1)
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