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Let X and Y have the following joint distribution: X \Y  0 1 2     0   2/12  1/12  5/12     1   1/12  1/12  2/12 (a) Find the probability distribution of X|Y = 0, and E[X|Y = 0]. (b) Find E[Y ] and E[X]. (c) Find the probability that Y is larger than zero. (d) Are X and Y dependent? Justify your answer

Let X and Y have the following joint distribution: X \Y  0 1 2     0   2/12  1/12  5/12     1   1/12  1/12  2/12 (a) Find the probability distribution of X|Y = 0, and E[X|Y = 0]. (b) Find E[Y ] and E[X]. (c) Find the probability that Y is larger than zero. (d) Are X and Y dependent? Justify your answer

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 21CR
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Let X and Y have the following joint distribution:
X \Y  0 1 2
    0   2/12  1/12  5/12
    1   1/12  1/12  2/12
(a) Find the probability distribution of X|Y = 0, and E[X|Y = 0].
(b) Find E[Y ] and E[X].
(c) Find the probability that Y is larger than zero.
(d) Are X and Y dependent? Justify your answer

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