Question: Let dependent random variables X, Y, and Z be defined by the joint distribution? which shows that Z is most likely to be the smallest.

Let dependent random variables X, Y, and Z be defined by the joint distribution?

P(X= minimum of X, Y, Z) = 0.25 P(Y=> minimum of X,

which shows that Z is most likely to be the smallest. What can you conclude? (See Blyth, 1972.)

P(X= minimum of X, Y, Z) = 0.25 P(Y=> minimum of X, Y, Z)=0.35 P(2 minimum of X, Y, Z) = 0.40

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