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?

Question

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&#039;t understand is why there is a condition of   P  {  Z  =  b      |    X  =  a  }. I couldn&#039;t find any known formula which can be used in this case. May you give me some hint, please?

giosgi5 · Accepted Answer

Explanation:  P  (  Z  =  b      |    X  =  a  )  =  P  (  a  ∨  Y  =  b      |    X  =  a  )  =  0 if   a  &amp;gt;  b and   P  (  Y  =  b  ) if   a  &amp;lt;  b. If   a  =  b you get   P  (  Y  ≤  b  )

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.

Answered question

Answer & Explanation

New Questions in High school geometry