Let X,Y be independent variables with geometric probability. Let Z=max{X,Y}. It is known that the joint probability of X,Z is P{X=a,Z=b}=P{X=a}P{Z=b|X=a} when a,b are nonzero integers.

bergvolk0k

bergvolk0k

Answered question

2022-10-24

Joint probability of X,max{X,Y}
Let X,Y be independent variables with geometric probability. Let Z = m a x { X , Y }.
It is known that the joint probability of X,Z is P { X = a , Z = b } = P { X = a } P { Z = b | X = a } when a,b are nonzero integers.
I am stuck here. What I can't understand is why there is a condition of P { Z = b | X = a }. I couldn't find any known formula which can be used in this case. May you give me some hint, please?

Answer & Explanation

giosgi5

giosgi5

Beginner2022-10-25Added 15 answers

Explanation:
P ( Z = b | X = a ) = P ( a Y = b | X = a ) = 0 if a > b and P ( Y = b ) if a < b. If a = b you get P ( Y b )

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