Probability (ISS Statistics Paper I (New 2016 MCQ Pattern)): Questions 82 - 84 of 205

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Question number: 82

» Probability » Probability Distributions » Uniform

MCQ▾

Question

If X1,X2,,Xn are i. i. d. uniform on [0,θ] , then if X¯=i=1nXin . Then Var (X¯) is________.

Choices

Choice (4) Response

a.

θ26n2

b.

θ26n

c.

θ212n2

d.

None of the above

Question number: 83

» Probability » Law of Total Probability

MCQ▾

Question

Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer are α and β respectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. What is the probability that A wins if B answers the first question?

Choices

Choice (4) Response

a.

β1(1α)(1β)

b.

(1α)β1(1α)(1β)

c.

(1β)α1(1α)(1β)

d.

α1(1α)(1β)

Question number: 84

» Probability » Bayes' Theorem and Applications

MCQ▾

Question

Suppose a certain drug test is 99 % sensitive and 99 % specific, that is, the test will correctly identify a drug user as testing positive 99 % of the time, and will correctly identify a non-user as testing negative 99 % of the time. Let’s assume a corporation decides to test its employees for drug use, and that only 0.5 % of the employees actually use the drug. The probability that, given a positive drug test, an employee is actually a drug user is conducted using Bayes’ theorem. Can we say Bayes’ theorem gives correct result?

Choices

Choice (4) Response

a.

Information insufficient

b.

Yes always

c.

Not always

d.

Can’t make any claim

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