Suppose that the heights of a parent and child, P and C in cm are jointly Gaussian
with
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.
There's the easy way and and there's the hard way. Being lazy by nature, I'll outline the key results for the easy way:
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:
where:
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