# Bivariate Normal Distribution Standard Error

Data from a large population indicate that the heights of mothers and daughters in this population follow a bivariate normal distribution with correlation 0.5. Both the mothers and daughters have a mean height of 5 ft 4in with a standard deviation on 2 inches.

Find a prediction for the daughter’s height if the mother’s height is 5 ft 10 in. Attach a standard error to this prediction.

I can predict the height but am completely lost when trying to compute the standard error attached to this prediction. Is this just the standard deviation? Thanks in advance.

• Yes I think so. The question seems just asking you about the conditional mean and standard deviation. Normally standard error will refer to standard deviation of an estimator. – BGM Apr 27 '17 at 4:51
• There is a surprising fast way to calculate the conditional standard deviation so long as you can manipulate the squares and square-roots: the square of the correlation represents what proportion of the variance of the dependent random variable results from the independent random variable. For a bivarate normal distribution this is not affected by the actual value of the independent random variable. – Henry Apr 27 '17 at 11:15