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 forms a similar pair) to each other if (the absolute value of) their height differences is less than 1/10. Let S be the sum of the heights for mothers and daughters over all similar pairs. Compute the expectation and the variance for S.Please express your answers exactly.

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