Suppose that the heights of a parent and child, P and C in cm are jointly Gaussian
mP = 170cm, standard deviation of P = 8cm
mC = 170cm, standard deviation of C = 8cm
correlation cofficient between P and C = 0.2
Find P[C>mC|P= mP], the probability that the child is above average height if the parent is average height.
If X and Y are jointly gaussian (bivariate normal distribution), then the conditional pdf for one of the variables, given a known value for the other variable, is normally distributed:
and is the correlation coefficient.
I'll leave it to you to substitute the necessary notation and values. It should then be routine to calculate .
Some reading: http://www.aos.wisc.edu/~dvimont/aos...iate_notes.pdf