Practice quiz2 and soln

Practice quiz2 and soln - AMS310.01 PREQUIZ 2 Practice...

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AMS310.01 PREQUIZ 2 Practice questions for quiz 2. _____ 1. P(A B)= 0.2 P(A)=0.5 P(B)= 0.6, P(B|A)= _______ 2. P(B|A) =0.5 P(A)=0.6 P(B)=0.8 P(A B)= ______ _______ 3. Given S= {1,2,3,4,5,6} the outcomes of the toss of 1 die. Let A={we get less than 5 dots} and let B={we get an even number of dots}. Which statement below is correct? (a) A and B independent events. A and B are mutually exclusive events. (b) A and B are dependent events. A and B are mutually exclusive event. (c) A and B are independent. A and B are not mutually exclusive. (d) A and B are dependent events. A and B are not mutually exclusive. ____ 4. Given the values below for F(x), the distribution function of X for all values of X for which f(x)=Pr(X=x)>0.0. Find Pr(X 2.5 ). Hint: F(x) = Pr({ X x}). x 0 0.5 1.0 1.5 2.0 2.5 3.0 F(x) 0.1 0.2 0.3 0.5 0.9 0.95 1.0 SOLUTIONS : 1. 2/5=0.4 1. P(A B)= 0.2 P(A)= 0.5 P(B)= 0.6, P(B|A)= SOLUTION : P(B|A) = P(A B)/P(A) = 0.2/0.5 = 0.4 2. 0.30___ 2. P(B|A) = 0.5 P(A)=0.6 P(B)=0.8 P(A B)= ______ SOLUTION : P(A B)= P(A|B) x P(B) = P(B|A) x P(A). Since we are given P(B|A) =0.5 and not given P(A|B) we calculate P(A B) = P(B|A)P(A) = 0.5 x 0.6 = 0.30.
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