(Solution Library) Let X 1 , X 2 ,…,X 10 be 10 independent Poisson random variables with mean 2. Let Y 1 be the number of X i ’s that are zero. Let Y 2
Question: Let X 1 , X 2 ,…,X 10 be 10 independent Poisson random variables with mean 2. Let Y 1 be the number of X i ’s that are zero. Let Y 2 be the number of the X i ’s that are one. Let Y 3 be the number of the X i ’s that are more than one.
-
Give the joint probability mass function of
Y
1
,
Y
2
, and
Y
3
, and determine
P(Y 1 = 1, Y 2 = 3, Y 3 = 6) - Specify the marginal distribution of Y 2 .
- Determine P(Y 1 = 2 | Y 3 = 6)
- Determine P(Y 2 = 3, Y 3 = 6)
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