Exercise:
　　Using the following joint probability distribution to answer the questions below：
 

 

Y=1

  Y=2

 Y=3

X=1

  0.05  

  0.05  

  0.10

X=2

  0.05  

  0.10  

  0.15

X=3

  0.15  

  0.15  

  0.20

 　　If you know that Y is equal to 2, the probability that X is equal to 1 is closest to:
　　A. 0.05
　　B. 0.25
　　C. 0.20
　　D. 0.17
　　Answer: D
　　Explanation:
 
　　相关知识点：Marginal, Conditional and Joint Probability Function
　　Marginal probability (unconditional probability) refers to the probability of an event regardless of the past or future occurrence of other events.
　　Conditional probability is one where the occurrence of one event affects the probability of the occurrence of another event. Using probability notation, “the probability of A given the occurrence of B” is expressed as P (A | B), where the vertical bar indicates “given”, or “conditional upon”.
　　The joint probability of two events is the probability that they will both occur. The joint probability of A and B, P(AB), is equal to the conditional probability of A given B, P (A | B), times the unconditional probability of B, P (B).

{C}{C}


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