State whether the following is always true (T) or not always true (F) a)V (4X −...
State whether the following is always true (T) or not always
true (F)
a)V (4X − 2Y ) = 16V (X) + 4V (Y ) + 8Cov(X, Y )
b)If X1, X2, ..., X100 are independent, normally distributed random variables, then the average X¯ = 1 100Σ 100 i=1Xi of these random variables is itself a random variable following a normal distribution.
c) If X and Y are random variables with a correlation of ρxy, Corr(2X, Y ) = 2ρxy
Homework Answers
TOPIC: Variance ,covariance,Sampling distribution of sample average from a Normal distribution,Correlation coefficient between variables.
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State whether the following is always true (T) or not always
true (F)
a)V (4X −...
1. (+1 each) State whether each of the following is always true (T) or not always true (a) If X...
1. (+1 each) State whether each of the following is always true (T) or not always true (a) If X1, X,X are drawn from the same population distribution, then X is ,Xn are not an unbiased estimator of the population mean μ, even if X1, X2, independent (b) Increasing the level a of a hypothesis test decreases the probability of rejecting the nul hypothesis. (c) A null hypothesis with a p-value of 0.02 is rejected at the 0.01 level. (e)...
Help please will give 5 stars and amazing feedback! TRUE OR FALSE AND WHY??? (g) Suppose...
Help please will give 5 stars
and amazing feedback! TRUE OR FALSE AND WHY???
(g) Suppose that E(Y | X) 1+2x and that E(X)-2. Then E(Y) 5 True False (h) Suppose that X1 and X2 are independent normal random variables with mean 0 and vari- ance 1. Then (X1 + X2)/2 is normally distributed with mean 0 and variance 1 True False
State whether each of the following are either always true (T) or not always true (F)
State whether each of the following are either always true (T)
or not always true (F)
(a) If you have two estimators for a parameter θ, with B(A) > B(92) and V(h) > V(92), then θ2 is consistent and θι is not consistent. (b) If Xi ~ Bernoulli(p) for i-: 1, , 1000, then Y-Σ21X, is normally distributed. (c) If you fail to reject a two-sided hypothesis test at the level a, then you wil also fail to reject a...
Which of the following statements is true? (a) If the calculated value of F statistic is...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
67. Explain why or why not Determine whether the following state- ments are true and give...
67. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. If f(x, y) x2 + y2 - 10, then Vf(x, y) = 2x + 2y b. Because the gradient gives the direction of maximum increase of a function, the gradient is always positive. c. The gradient of f(x, y, z) = 1 + xyz has four components d. If f(x, y, z) = 4, then Vf = 0
Show steps, thanks ·Additional Problem 13. For random variables X and Y it is given that...
Show steps, thanks
·Additional Problem 13. For random variables X and Y it is given that Ox = 2, ơY = 5, and pxy 3 (a) Find Cov(Xx,y) (b) Var(4X-2Y7 Answers: (a) -. (b) 002 10652 li 3 . Additional Problem 14. Suppose Xi and X2 are independent random variables that have exponential distribution with β 4. (a) Find the covariance and correlation between 5Xi + 3X, and 7Xi-2X. (b) Find Var-5X2-2
4 persons each have playing cards, with person 1 having X1 cards, person 2 having X2...
4 persons each have playing cards, with person 1 having X1 cards, person 2 having X2 cards, person three having X3 cards and person 4 having X4 cards. The random variables of X1, X2, X3 and X4 are all independent and normally distributed with mean = 100 and SD = 24. 1) If Y = X1+X2+X3+X4 (all the cards of alle the persons), what is then E(Y)? What is Var(Y)? 2) Denoting A as the average no. of cards per...
4. Use the distribution function technique to find the density function for Y = 2X +...
4. Use the distribution function technique to find the density function for Y = 2X + 3 The density function for X is f(x). Your answer should be given as a piecewise function. 2x + 1) 1<x<2 f(x) = 4 0 elsewhere =f2x+1) h 5. Use the transformation technique to find the density function for Y = 4x + 1. The density function for X is f(x). Your answer should be a piecewise function. f(x) = S4e-4x 0 < x...
Express the system of differential equations in matrix notation x – 4x + y - (cos...
Express the system of differential equations in matrix notation x – 4x + y - (cos t)x = 0 y"+y" - t?x' + 3y'+e-2x = 0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. Xi =X, X2 = X". X3 = y, Xa =y" O B. *= x, X2 = x', *3 = y, X4 =y', X5 =y" OC. *1 =...
1. True or False: (1pt each) (T) (F) If a distribution is normal, then it is...
1. True or False: (1pt each) (T) (F) If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean. (T) (F) Normal distribution is a discreet probability distribution for a random variable. (T) (F) If the variable follows a binomial distribution, then about 68 % of the variables are within 1 SD of the mean, about 95% of the variables are within +2 SD of the...
1. (+1 each) State whether each of the following is always true (T) or not always true (a) If X1, X,X are drawn from the same population distribution, then X is ,Xn are not an unbiased estimator of the population mean μ, even if X1, X2, independent (b) Increasing the level a of a hypothesis test decreases the probability of rejecting the nul hypothesis. (c) A null hypothesis with a p-value of 0.02 is rejected at the 0.01 level. (e)...
Help please will give 5 stars
and amazing feedback! TRUE OR FALSE AND WHY???
(g) Suppose that E(Y | X) 1+2x and that E(X)-2. Then E(Y) 5 True False (h) Suppose that X1 and X2 are independent normal random variables with mean 0 and vari- ance 1. Then (X1 + X2)/2 is normally distributed with mean 0 and variance 1 True False
State whether each of the following are either always true (T)
or not always true (F)
(a) If you have two estimators for a parameter θ, with B(A) > B(92) and V(h) > V(92), then θ2 is consistent and θι is not consistent. (b) If Xi ~ Bernoulli(p) for i-: 1, , 1000, then Y-Σ21X, is normally distributed. (c) If you fail to reject a two-sided hypothesis test at the level a, then you wil also fail to reject a...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
67. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. If f(x, y) x2 + y2 - 10, then Vf(x, y) = 2x + 2y b. Because the gradient gives the direction of maximum increase of a function, the gradient is always positive. c. The gradient of f(x, y, z) = 1 + xyz has four components d. If f(x, y, z) = 4, then Vf = 0
Show steps, thanks
·Additional Problem 13. For random variables X and Y it is given that Ox = 2, ơY = 5, and pxy 3 (a) Find Cov(Xx,y) (b) Var(4X-2Y7 Answers: (a) -. (b) 002 10652 li 3 . Additional Problem 14. Suppose Xi and X2 are independent random variables that have exponential distribution with β 4. (a) Find the covariance and correlation between 5Xi + 3X, and 7Xi-2X. (b) Find Var-5X2-2
4. Use the distribution function technique to find the density function for Y = 2X + 3 The density function for X is f(x). Your answer should be given as a piecewise function. 2x + 1) 1<x<2 f(x) = 4 0 elsewhere =f2x+1) h 5. Use the transformation technique to find the density function for Y = 4x + 1. The density function for X is f(x). Your answer should be a piecewise function. f(x) = S4e-4x 0 < x...
Express the system of differential equations in matrix notation x – 4x + y - (cos t)x = 0 y"+y" - t?x' + 3y'+e-2x = 0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. Xi =X, X2 = X". X3 = y, Xa =y" O B. *= x, X2 = x', *3 = y, X4 =y', X5 =y" OC. *1 =...
1. True or False: (1pt each) (T) (F) If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean. (T) (F) Normal distribution is a discreet probability distribution for a random variable. (T) (F) If the variable follows a binomial distribution, then about 68 % of the variables are within 1 SD of the mean, about 95% of the variables are within +2 SD of the...
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