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##### PSTAT 109 Statistics for Economics Midterm Exam Winter 2014

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Question;Review Midterm Exam: PSTAT109, Feb., 2014.;There is only one correct answer in each multiple choice questions;#1,#2,#3.;1. Let P be a;probability and let A, B, C be any events. Then;(a)P(A\B\C) =P(A)P(B)P(C);(b)P(A[B[C) =P(A) +P(B) +P(C);(c)P(A) =P(A\C) +P(A\CC);(d)P(A[B[C) = 1;2. Let P be a;probability and let A and B be;two independent events. Then;(a)P(A[B) =P(A) +P(B);(b)P(A\B) =P(A[B)????P(A);(c)P(AC\B) =P(AC)P(B);(d) none of the;previous answers;3. LetPbe a;probability and letAandBbe;two events. If the random variableXis;de.ned byX=1A+ 2_1Bthen;(a)E[X] =P(A\B);(b)X_1A\B= 3_1A\B;(c)E[X] =P(A) +P(B);(d) none of the;previous answers;4. In a class, 60% of;students have an Apple account, 50% have a Google+ account and 30% have both.;(a) How many (in;percentage) don.t have either?;(b) How many (in;percentage) have and Apple account but not a Google+ account?;5. In how many;di?erent ways 5 people can sleep in a house with 3 rooms (one person per room;and only 3 people can sleep in the house)?;6. How many di?erent;committees of 3 members can be formed out of a group of 7 people.;7. Suppose a class;contains 60% girls and 40% boys. Suppose that 20% of the girls have blue eyes;and 10 % of the boys have blue eyes. What is the probability that a randomly;chosen student has blue eyes?;8. Suppose that: the;probability of snow is 20%, the probability of a tra? c accident is 10%, the;conditional probability of an accident given that it snows is 40%. What is the;conditional probability that it snow given that there is an accident?;9. You.ip 8 fair;coins. Count the number of sequences with exactly 3 Tails.;10. Write the;de.nition of the variance of a random variable and 3 of its properties.;11. LetPbe a;probability and letAbe any event in the sample space. Prove that;P(AC) = 1????P(A)

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