Multiple Random Variables & OperationsUnit-2. MULTIPLE CHOICE 1 2 3 4 5 6 7 8 9 10 TRUE OR FALSE 11 12 13 14 15 FILL IN THE BLANKS 16 17 18 19 20 Multiple.

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Presentation transcript:

Multiple Random Variables & OperationsUnit-2

MULTIPLE CHOICE TRUE OR FALSE FILL IN THE BLANKS Multiple Random Variables & OperationsUnit-2

Multiple Random Variables & Operations MULTIPLE CHOICE 1.m 10 is ………………….Order Moment[] (A) Zero(B) First (C) Second(D) Third

Multiple Random Variables & Operations MULTIPLE CHOICE 2. m 11 is ………………….Order Moment[] (A) Zero(B) First (C) Second(D) Third

Multiple Random Variables & Operations MULTIPLE CHOICE 3. The correlation of two Random Variables X and Y is ………………Order Moment[] (A) Zero(B) First (C) Second(D) Third

Multiple Random Variables & Operations MULTIPLE CHOICE 4. If two Random Variables X and Y are Orthogonal, then their correlation is………….[] (A) Zero(B) +1 (C) -1(D) Infinite

Multiple Random Variables & Operations MULTIPLE CHOICE 5. The covariance of two Random Variables X and Y is ………… Order central Moment[] (A) Zero(B) First (C) Second(D) Third

Multiple Random Variables & Operations MULTIPLE CHOICE 6. The Normalized second order central moment is called as …………….[] (A) Density(B) Correlation (C) Covariance (D) Correlation coefficient

Multiple Random Variables & Operations MULTIPLE CHOICE 7. If two random variables X and Y are independent, then the covariance is………….[] (A) Infinite(B) +1 (C) -1(D) Zero

Multiple Random Variables & Operations MULTIPLE CHOICE 8. For two random variables X and Y, Var(X-Y)= …………… [] (A) Var(X) + Var(Y) + C XY (B) Var(X) + Var(Y) - C XY (C) Var(X) + Var(Y) - 2C XY (D) Var(X) + Var(Y) + 2C XY

Multiple Random Variables & Operations MULTIPLE CHOICE 9. For two random variables X and Y, cov(aX, bY) = ……………[] (A) aC XY + bC XY (B) (a+ b)C XY (C) (a- b)C XY (D) abC XY

Multiple Random Variables & Operations MULTIPLE CHOICE 10. Gaussian random variables are completely defined from their…………………….[] (A) means(B) variances (C) covariances(D) All the above

Multiple Random Variables & Operations TRUE OR FALSE 11. If Gaussian random variables are uncorrelated, then they are statistically independent.[]

Multiple Random Variables & Operations TRUE OR FALSE 12. The linear transformations of Gaussian random variables are not Gaussian.[]

Multiple Random Variables & Operations TRUE OR FALSE 13. cov ( X + a, Y + b) = cov (X,Y) []

Multiple Random Variables & Operations TRUE OR FALSE 14. If X and Y are two random variables, then the covariance is C XY = R XY []

Multiple Random Variables & Operations TRUE OR FALSE 15. If C XY = 0 then the two random variables and X and Y are independent.[]

Multiple Random Variables & Operations FILL IN THE BLANKS 16. The joint moments from the joint characteristic function are given by m nk = …………………..

Multiple Random Variables & Operations FILL IN THE BLANKS 17. The joint moments from the joint moment generating function are given by m nk = …………………..

Multiple Random Variables & Operations FILL IN THE BLANKS 18. For continuous random variables X and Y, the second order central moment R xy = m 11 = E[XY]=…………………..

Multiple Random Variables & Operations FILL IN THE BLANKS 19. The correlation coefficient or covariance coefficient denoted as is given by, = …………………

Multiple Random Variables & Operations FILL IN THE BLANKS 20. The density function for N number of discrete Gaussian random variables is given by f X1,X2…XN (x 1,x 2 …x N ) = ………….…………

MULTIPLE CHOICE 1B 2C 3C 4A 5C 6D 7D 8C 9D 10D TRUE OR FALSE 11TRUE 12FALSE 13TRUE 14FALSE 15FALSE FILL IN THE BLANKS Answers