ECE302 Quiz-08

What is the joint probability mass function (PMF) of two discrete random variables X and Y defined as?

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

CCSS.HSS.CP.B.8

How do you calculate the marginal probability density function (PDF) f_X(x) from the joint PDF f_X,Y​(x,y)?

If two random variables X and Y are independent, how is their joint PDF f_X,Y(x,y) related to their marginal PDFs?

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.8

What is the joint expectation E[XY] of two continuous random variables X and Y?

What does the joint expectation E[XY] represent?

• The covariance between X and Y

• A weighted inner product between the states of X and Y

• The variance of the sum of X and Y

• The sum of the individual expectations of X and Y

What inequality holds for the joint expectation E[XY] according to the Cauchy-Schwarz inequality?

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

What is the formula for the covariance of two random variables X and Y?

Tags

CCSS.HSS.ID.B.6

What is the correlation coefficient between two random variables X and Y?

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

If two random variables X and Y are independent, what can be said about their covariance?