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Math Help - Continuous Random Variables

  1. #1
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    Continuous Random Variables

    Hi could anyone check if I have done the following questions correctly and also help me out with a couple:

    The random variable X has N(2,3) distribution. Evaluate:

    (i) P( X > 3 )
    (ii) P(-1 < X < 4 )
    (iii) Find a, such that P( (X-2) < a ) = 0.1


    So for part (i) I have P(Z> (1/root3) )
    and for part (ii) i have P( Z < (2/root3) - P (Z < -3/root3)


    Second question is:

    The random variables X and Y are independent N(1,5) and N(5,1).

    Evaluate:
    (i) P( X < 0, Y > 6) and
    (ii) P ( -3 < 3X - Y < 0)

    Thanks.
    Last edited by axa121; November 1st 2009 at 10:02 AM.
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  2. #2
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    Quote Originally Posted by axa121 View Post
    Hi could anyone check if I have done the following questions correctly and also help me out with a couple:

    The random variable X has N(2,3) distribution. Evaluate:

    (i) P( X > 3 )
    (ii) P(-1 < X < 4 )
    (iii) Find a, such that P( (X-2) < a ) = 0.1


    So for part (i) I have P(Z> (1/root3) )
    and for part (ii) i have P( Z < (2/root3) - P (Z < -3/root3) Mr F says: Once you have the z-values you should have been taught how to use standard normal tables to get the required probabilities (look in your classnotes or textbook).

    Second question is:

    The random variables X and Y are independent N(1,5) and N(5,1).

    Evaluate:
    (i) P( X < 0, Y > 6) and
    (ii) P ( -3 < 3X - Y < 0)

    Thanks.
    (i) Pr( X < 0) times Pr(Y > 6).

    (ii) Since X and Y are independent, W = 3X - Y follows a normal distribution with mean 3E(X) - E(Y) and variance 3^2Var(X) + 1^2 Var(Y) (see property 1 here Normal distribution - Wikipedia, the free encyclopedia). So calculate Pr(-3 < W < 0) in the usual way.
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  3. #3
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    Yep, I do have the tables. I just wanted to know whether the Z values were correct.

    Thanks, I will the second question and post my answers.
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