Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and Y always take on the same value. (a) Do X and Y have the same PMF? (b) Is it possible for X and Y to be independent?

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Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and Y always take on the same value.

(a) Do X and Y have the same PMF? (b) Is it possible for X and Y to be independent?

Answered Same DayDec 26, 2021

Answer To: Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and Y always take on...

David answered on Dec 26 2021

114 Votes

Ans. 1
For the given discrete problem,
The condition of probability,
( ) ( ) 1
and,
P X P Y
X Y
 


a)
This condition will be probability mass function (PMF),
If, 0 1P  , ( ) 1ii P x 
It means the value of probability is same.
It can also be written as, ( ) ( )X s Y s...

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Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and Y always take on the same value. (a) Do X and Y have the same PMF? (b) Is it possible for X and Y to be independent?

Answer To: Suppose X and Y are discrete r.v.s such that P(X = Y ) = 1. This means that X and Y always take on...

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