. Xand Y are random variables, and f(') is the corresponding probability function. Which of the following is/are true?

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10. X and Yare random variables, and f() is the corresponding probability function. Which of the following is/are true?
If X and Y are independent, then fx(x) 2 0, fy(y) 2 0, and fx y(x, y) = fx(x) fy(y) for all values of x & y.
Regardless of whether X and Y are independent, fx(x) s 0, fy(y) s 0, and fx y(x, y) 2 0 for all values of x & y.
If X and Y are positively correlated, then fx y(x, y) < fx(x) fy(y) for all values of x & y.
If X and Y are negatively correlated, then fx y(x, y) < fx(x) fy(y) for all values of x & y.
Transcribed Image Text:10. X and Yare random variables, and f() is the corresponding probability function. Which of the following is/are true? If X and Y are independent, then fx(x) 2 0, fy(y) 2 0, and fx y(x, y) = fx(x) fy(y) for all values of x & y. Regardless of whether X and Y are independent, fx(x) s 0, fy(y) s 0, and fx y(x, y) 2 0 for all values of x & y. If X and Y are positively correlated, then fx y(x, y) < fx(x) fy(y) for all values of x & y. If X and Y are negatively correlated, then fx y(x, y) < fx(x) fy(y) for all values of x & y.
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