When figure skaters need to find a partner for “pair figure skating,” it is impo

Question

When figure skaters need to find a partner for “pair figure skating,” it is important to find a partner who is compatible in weight. The weight of figure skaters of all pairs can be modeled by a Normal distribution on both gender. For male skaters, the mean is 165 pounds with a standard deviation of 15 pounds. For female skaters, the mean is 100 pounds with a standard deviation of 10 pounds. The correlation between X and Y equals to 0.8. Let X = the weight of male skaters and Y = the weight of female skaters. And let W = X - Y. Then W has a Normal distribution. What are the mean and standard deviation of W?  

Explanation / Answer

here mean of W =165-100=65

and std deviation of W =(var(X)+Var(Y)-2*r*(Var(X)Var(Y))1/2 )=(152+102-2*0.8*(15*10))1/2 =9.2195

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