Following Galton let us assume that the fathers and sons have heights that are d

Following Galton let us assume that the fathers and sons
have heights that are dependent normal random variables. Assume that the
average height is 68 inches standard deviation is 2.7 inches and the
correlation coefficient is .5 That is
assume that the heights of the fathers and sons have the form 2.7X + 68 and 2.7Y
+ 68 respectively where X and Y are correlated standardized normal random
variables with correlation coefficient .5.(a) What is the expected height for the son of a father
whose height is 72 inches?(b) Plot a scatter diagram of the heights of 1000 father and
son pairs. Hint:You can choose standardized pairs as in Exercise 23 and then
plot (2.7X+ 68 2.7Y + 68).