Question

In: Statistics and Probability

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation...

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1

. Find the correlation coefficient ρX,Y .

5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?

Solutions

Expert Solution

4. The correlation (or correlation coefficient) between random variables X and Y , denoted as ρXY , is

where

Covariance (i.e. σXY ) is an expected value of a function of X and Y over the (X, Y ) space, if X and Y are continuous we can write

or

and

orchestra answered 2 years ago
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