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1. Suppose X has mean 3 and variance 4, Y has mean 5 and variance 9,...
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What...
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What is F(-5)? (c) Compute the p.d.f of X. (d) Compute the mean of X (e) Compute the variance of X. (f) Compute the standard deviation of X (g) Compute the squared coefficient of variation of X.
3. Suppose the covariance between Y and X is 15, the variance of Y is 25,...
3. Suppose the covariance between Y and X is 15, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X? 4. Compare and contrast covariance between Y and X is 10 and covariance between P and Q is 1,210
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine...
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y])2? (c) Compute PríY <5) (d) Compute PríY >5 Y >1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that PriY >
7. X is a random variable with a mean of 2 and a variance of 3,...
7. X is a random variable with a mean of 2 and a variance of 3, and Y is a random variable with a mean of 4 and a variance of 5, and the covariance between X and Y is -3. Define (a) Find the expected value of W. b) Find the variance of W
5. Suppose the random variables X, Y and Z are related through the model Y =...
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + 2, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X,Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3)....
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3). (b) Find P(1 < X < 3) (c) Find P({X > 4}|{X > 3}) (d) Let Y = X^2 . Find E[Y].
Let Y be a random variable with p.d.f. ce-4y for y ≥ 0. (a) Determine c....
Let Y be a random variable with p.d.f. ce-4y for y ≥ 0. (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y )/(E[Y ])2? (c) Compute Pr{Y < 5}. (d) ComputePr{Y >5|Y >1}. (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that Pr{Y > q} = 0.7?
5. Suppose the random variables X, Y and Z are related through the model Y =...
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b)...
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y)2? (c) Compute PríY < 5) (d) Compute PrY >5 |Y>1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that Pr(Y > q} 0.7?
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according...
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What is F(-5)? (c) Compute the p.d.f of X. (d) Compute the mean of X (e) Compute the variance of X. (f) Compute the standard deviation of X (g) Compute the squared coefficient of variation of X.
3. Suppose the covariance between Y and X is 15, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X? 4. Compare and contrast covariance between Y and X is 10 and covariance between P and Q is 1,210
6. Let Y be a random variable with p.d.f. ce4y for y 2 0 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y])2? (c) Compute PríY <5) (d) Compute PríY >5 Y >1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that PriY >
7. X is a random variable with a mean of 2 and a variance of 3, and Y is a random variable with a mean of 4 and a variance of 5, and the covariance between X and Y is -3. Define (a) Find the expected value of W. b) Find the variance of W
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + 2, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X,Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
5. Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance o2 = 16 and X has variance of = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter
6. Let Y be a random variable with p.d.f. ce-4y for y20 (a) Determine c. (b) What is the mean, variance, and squared coefficient of variation of Y where the squared coefficient of variation of Y is defined to Var(Y)/(E[Y)2? (c) Compute PríY < 5) (d) Compute PrY >5 |Y>1) (e) What is the 0.7 quantile (or 70th percentile) where the 0.7 quantile is the point q such that Pr(Y > q} 0.7?
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
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