Let X and Y be the number of tables and chairs in an office. p(x, y) of X and Y is given in the table. 2 11 3

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Chapter1: Combinatorial Analysis
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|Let X and Y be the number of tables and chairs in an office.
The joint pmf p(x, y) of X and Y is given in the table.
y = 0| y = 1 y = 2 y = 3
x = 1
x = 2
0.05
0.06
0.10
0.14
0.05
0.10
0.20
0.30
(a) Find the probability P(X + Y < 4).
(b) Find the conditional probability P(X = 1|Y = 2). Are X and Y inde-
pendent or not?
(c)
Find the expected value E(X +Y).
Transcribed Image Text:|Let X and Y be the number of tables and chairs in an office. The joint pmf p(x, y) of X and Y is given in the table. y = 0| y = 1 y = 2 y = 3 x = 1 x = 2 0.05 0.06 0.10 0.14 0.05 0.10 0.20 0.30 (a) Find the probability P(X + Y < 4). (b) Find the conditional probability P(X = 1|Y = 2). Are X and Y inde- pendent or not? (c) Find the expected value E(X +Y).
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