Suppose that 100 pairs of mother and daughter participate in a social study.

Suppose that the standardized heights for the mother and for the daughter jointly have a standard bivariate normal distribution with correlation = 3/4, and suppose that the heights for different (mother-daughter) pairs are independent.

We say that the mother and her daughter are similar (in this case, the mother and her daughter form a similar pair) to each other if (the absolute value of) their height differences are less than 1/10.

Let S be the sum of the heights for mothers and daughters overall similar pairs.

Compute the expectation and the variance for S.

(Please express your answers exactly.)