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Table 4-6- Joint distribution- Assume that the random variables X and.docx

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The joint distribution of random variables X and Y is given in a table. The probability that X=1 and Y=0 can be read directly from the table. The conditional probability that Y=0 given X=2 can also be calculated from the values in the table. Whether X and Y are independent can be determined by comparing their joint distribution to their marginal distributions. The distribution of the new random variable Z=XY is defined by the values of X and Y in the table.

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Table 4.6: Joint distribution. Assume that the random variables X and Y have the joint distribution given in Table 4.6 . (a) What is P ( X 1 and Y 0 ) ? (b) What is the conditional probability that Y 0 given that X = 2 ? (c) Are X and Y independent? (d) What is the distribution of Z = X Y ?

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Table 4-6- Joint distribution- Assume that the random variables X and.docx

  • 1. Table 4.6: Joint distribution. Assume that the random variables X and Y have the joint distribution given in Table 4.6 . (a) What is P ( X 1 and Y 0 ) ? (b) What is the conditional probability that Y 0 given that X = 2 ? (c) Are X and Y independent? (d) What is the distribution of Z = X Y ?