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For random variables X and Y, and constants a, b, and c: E(a+bX+cY)= A. a+bE(X)+cE(Y) B .bE(X)+cE(Y) C .a+b+c D .Asymptotic theory A.

4.For random variables X and Y, and constants a, b, and c: E(a+bX+cY)=

A. a+bE(X)+cE(Y)

B .bE(X)+cE(Y)

C .a+b+c

D .a

5.Asymptotic theory

A.shows that at least basic statistical techniques (estimation; confidence intervals) remain accurate even when assumptions are violated in finite samples.

B. can be empirically tested, if not mathematically proved.

C. helps us approximate finite-sample properties.

D. is useful only if we plan to continue gathering more and more data in the future.

6.Let X be a random variable measuring pre-tax earnings in dollars, and let after-tax earnings Y be the function Y = \$2000 + 0.8 X. If E(X)=\$50,000 and Var(X)=4×108dollars2, then what is the mean after-tax earnings?

A.\$52,000

B.\$42,000

C.\$2,000

D.\$50,000

7.Let Z be a random variable with a standard normal distribution, N(0,1). What is P(Z<0)?

A.0

B.0.4

C.0.5

D.0.49

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