Let X be a uniform random variable in the interval (0,1). A coin is tossed twice and
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Let X be a uniform random variable in the interval (0,1). A coin is tossed twice and the results are denoted by Y1, Y2. Denote by 1 the outcome head and by 0 the outcome tail. We assume that the probability of heads is x and Y1, Y2 are independent if X is given. In particular, P(Y1=1,Y2=0∣X=x)=x(1−x),x∈(0,1).
(i) Compute P(Y1=1,Y2=0)
(ii) Compute the pdf of X given the event {Y1=1,Y2=0} .
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College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
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