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
TOPIC: Variance ,covariance,Sampling distribution of sample average from a Normal distribution,Correlation coefficient between variables.
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 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 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 + 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...