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Math Help - Bivariate Normal Distribution Problem

  1. #1
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    Bivariate Normal Distribution Problem

    I am little bit confused with the conditional probabilities in the following problem.


    The correlation coefficient between the heights of husbands and wives is 0.70 and the male height is 5 feet 10 inches with standard deviation 2 inches, and the mean female height is 5 feet 4 inches with standard deviation 1.5 inches. Assuming a bivariate normal distribution, what is the best guess of the height of a woman whose husband's height is 6 feet? Find a 95% prediction interval for her height.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by akolman View Post
    I am little bit confused with the conditional probabilities in the following problem.


    The correlation coefficient between the heights of husbands and wives is 0.70 and the male height is 5 feet 10 inches with standard deviation 2 inches, and the mean female height is 5 feet 4 inches with standard deviation 1.5 inches. Assuming a bivariate normal distribution, what is the best guess of the height of a woman whose husband's height is 6 feet? Find a 95% prediction interval for her height.

    Thanks in advance.
    The joint pdf f(x, y) can be constructed easily from the given data. Now find f(y | x) = \frac{f(x, y)}{f_X(x)} where f_X(x) is the marginal pdf of X and substitute x = 6 feet.

    Use this conditional pdf to answer the questions (I imagine best guess for height of woman is the mean of this pdf).
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