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March 27, 2017

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Three cards are randomly chosen, without replacement, from a standard deck of
52. The random variable X represents the number of hearts cards chosen.
Construct the probability distribution for X.

  • statistics - ,

    Sample space, S={0,1,2,3}

    PDF:
    -∞<X<0 P(X)=0
    P(0)=39*38*37/3! /C(52,3) no heart
    P(1)=13*39*38/2! /C(52,3) 1 heart, 2 cards of other suits
    P(2)=13*12/2!*39 /C(52,3) 2 hearts, 1 card of other suits
    P(3)=13*12*11/3! /C(52,3) 3 hearts
    3<X<∞ P(X)=0

    Make sure that the values of the discrete PDF add up to 1.

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