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Which of the following hold(s) for random variables X and...
Answer can be one or multiple Which of the following always hold(s) for correlation coefficient pxy...
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Which of the following always hold(s) for correlation coefficient pxy of two random variables? 。pxY always lies between 0 and 1 。pxY always lies between-1 and 1 。PXY cannot be 1 PXY cannot be O
Answer can be one or multiple Which of the following statements are true about all Independent...
Answer can be one or multiple
Which of the following statements are true about all Independent random variables, X and Y? V(X+ Y) = V(X) + V(Y)
Question 1: Which one of the following statements does NOT hold true for ALL random variables...
Question 1: Which one of the following statements does NOT hold true for ALL random variables X, Y? I. E(X-2Y ) = E (X)-2E(Y) 2, Var (-X)=Var (X) 3. E (XY) E (X)E(Y) 4. Var (Y-1)=Var (Y) Question 2: Assume that X and Y are independent. Which one of the following statements is always true? I. If X = 0 then Y =0 2. If X = 0 then Y *0 3. P(X=1,Y=1)=P(X=1),P(Y=1) Question 3: Which one of the following...
Problem 1. (6pt) A discrete random variable X can take one of three different values z1,...
Problem 1. (6pt) A discrete random variable X can take one of three different values z1, z and z probabilities ¼, ½ and ¼ respectively, and another random variable Y can 1. 32 and ys, also with probabilities 4V2 and /4, respectively, as shown in the the relative frequency with which some of those values are jointly taken is also shown in the following table with take one of three distinct values P2 P14 (a) (Spt) From the data given...
Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The...
Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The probability distribution function is p(x) = Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ∼ N(0, 1). X and Y are independent. Meanwhile, let Z = XY . (a) What is the Expectation (mean value) of X? (b) Are Y and Z independent? (Just clarify, do not need to prove) (c) Show that Z is also a standard...
C y Multiple Choice Question Consider the discrete random variables X and Y with the following...
C y Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability nass function: fxy(x, y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding
Consider the discrete random variables X and Y with the following joint probability mass function: 2...
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
help asap pls T 6. Multiple Choice Question Consider the discrete random variables X and Y...
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T 6. Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: y fxx (2,y) -1 0 1/8 0 - 1 1/4 0 1/4 0 1/8 -1 1/8 1 1/8 What is P(X = 11Y = 0)? Are X and Y independent? 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y )...
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
The answer can be one or many of the choices. Which of the following statements are...
The answer can be one or many of the choices.
Which of the following statements are true for all random variables X, Y and fixed numbers a, bE R? O lfEX + a]=E[X+8, then a = b. If E[aX] = ElbX), then a=b.
Answer can be one or multiple
Which of the following always hold(s) for correlation coefficient pxy of two random variables? 。pxY always lies between 0 and 1 。pxY always lies between-1 and 1 。PXY cannot be 1 PXY cannot be O
Answer can be one or multiple
Which of the following statements are true about all Independent random variables, X and Y? V(X+ Y) = V(X) + V(Y)
Question 1: Which one of the following statements does NOT hold true for ALL random variables X, Y? I. E(X-2Y ) = E (X)-2E(Y) 2, Var (-X)=Var (X) 3. E (XY) E (X)E(Y) 4. Var (Y-1)=Var (Y) Question 2: Assume that X and Y are independent. Which one of the following statements is always true? I. If X = 0 then Y =0 2. If X = 0 then Y *0 3. P(X=1,Y=1)=P(X=1),P(Y=1) Question 3: Which one of the following...
Problem 1. (6pt) A discrete random variable X can take one of three different values z1, z and z probabilities ¼, ½ and ¼ respectively, and another random variable Y can 1. 32 and ys, also with probabilities 4V2 and /4, respectively, as shown in the the relative frequency with which some of those values are jointly taken is also shown in the following table with take one of three distinct values P2 P14 (a) (Spt) From the data given...
C y Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability nass function: fxy(x, y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
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T 6. Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: y fxx (2,y) -1 0 1/8 0 - 1 1/4 0 1/4 0 1/8 -1 1/8 1 1/8 What is P(X = 11Y = 0)? Are X and Y independent? 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
The answer can be one or many of the choices.
Which of the following statements are true for all random variables X, Y and fixed numbers a, bE R? O lfEX + a]=E[X+8, then a = b. If E[aX] = ElbX), then a=b.
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