Suppose that Z is a discrete random variable with Var(Z) = 1/2 a quantities. %3D Var(2 – Z) Drag answer here Var(3Z) Drag answer here Var(67²) Drag answer here

2. Need help

Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and variance of 2. Let S=X+Y, calculate E(S) and Var(S). Let Z=2Y^2+1/2 X+1 calculate E(Z). Hint: for any random variable X, we have Var(X)=E(X-E(X))^2=E(X^2 )-(E(X))^2, you may want to find EY^2  with this. Calculate cov(S,X). Hint: similarly, we have cov(Z,X)=E(ZX)-E(Z)E(X), Calculate cov(Z,X). Are Z and X independent? Are Z and Y independent? Why? What about mean independence?

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Determine the mean and the variance for the (continuous) random variables with the following moment-generating function: M(t) = (1 – 4t)-2

X and Y are random variables that are the same normally distributed variables as in the previous problem. The Mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter. The mean of T= - 3x + 20 is The mean of W= Y - X is The variance of D= X - 2Y is

2. Confidence interval σ knownDr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed a normal distribution with the population standard deviation of 2.4a words per essay. For her Tuesday class of 40 students, the mean number of misspelled words per essay was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of students’ essays. (a=1)

Suppose that X is a random variable for which the m.g.f. is as follows: M(t) = 1/4(3et+e-t), -∞<t<∞  Find the mean and variance of X.

Let X1 and X2 be two independent random variables with common mean E(X1) = E(X2) = µ. The variance of X1 is 1 and the variance of X2 is 16. Consider estimators of u described by û = W1X1 + W2X2 for some constants w1 and w2 that you can choose. (a) Say that w2 the estimate unbiased for all w1? = a – bw1 for some constants a and b. What values of a and b would make

Find variance of Y1