Suppose that the random variables X, Y , and Z have the following joint probability distribution. Determine

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Suppose that the random variables X, Y , and Z have the following joint probability distribution.

х f(x, y, z) 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 0.20 1 0.20 2 1 0.15 2 1 0.10 2 2 0.05


Determine the following:

(a) P(X = 2) 

(b) P(X = 1, Y = 2)

(c) P(Z <1.5) 

(d) P(X = 1 or Z = 2)

(e) E(X ) 

(f) P(X = 1|Y = 1)

(g) P(X = 1, Y = 1| Z = 2) 

(h) P(X = 1|Y = 1, Z = 2)

(i) Conditional probability distribution of X given that Y = 1 and Z = 2

Distribution
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Applied Statistics And Probability For Engineers

ISBN: 9781118539712

6th Edition

Authors: Douglas C. Montgomery, George C. Runger

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