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Math Help - random varibales

  1. #1
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    random varibales

    Suppose that Y1 and Y2 are independent Normal random variables with means and variances
    (m1, s1^2) and (m2, s2^2) respectively. Let X1 = Y1 + Y2 and X2 = Y1 - Y2. Show that X1 is
    normally distributed with mean and variance given by (m1 + m2 , s1^2+s2^2). What can you
    say about the distribution of X2?

    Thanks for answer
    and can you plz tell me what i have to study and from where bcoz i missed a whole week lecture
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  2. #2
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    Quote Originally Posted by anitaK View Post
    Suppose that Y1 and Y2 are independent Normal random variables with means and variances
    (m1, s1^2) and (m2, s2^2) respectively. Let X1 = Y1 + Y2 and X2 = Y1 - Y2. Show that X1 is
    normally distributed with mean and variance given by (m1 + m2 , s1^2+s2^2). What can you
    say about the distribution of X2?

    Thanks for answer
    and can you plz tell me what i have to study and from where bcoz i missed a whole week lecture
    There are several ways of "Show[ing] that X1 is normally distributed with mean and variance given by (m1 + m2 , s1^2+s2^2)."

    Read PlanetMath: moment generating function of the sum of independent random variables and http://www.math.umd.edu/~jjm/momentg...gfunctions.pdf (theorem 18).

    Also read Sum of normally distributed random variables - Wikipedia, the free encyclopedia.


    There are several approaches for "What can you say about the distribution of X2?" Note that if Y2 is a normal random variable with mean m2 and variance s2^2, then -Y2 is a normal random variable with mean -m2 and variance s2^2 .....
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