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We have two random variables $X$ and $Y$ both of them follows Binomial Distribution with parameters $n$ and $0.5$. Consider, another random variables, $Z$ which is also Binomial Distribution with parameters $2n$ and $0.5$.

Then, represent the probability of $P(X=Y)$ in terms of probability of $Z$.

My approach

Clearly, the random variable, $Z$ is the sum of $X$ and $Y$ random variables. So,

$P(X=Y) = P(X-Y=0)$ which can only happen when both $X$ and $Y$ is zero. Hence,

$P(X-Y=0)=P(X=0)P(Y=0)=(\frac{1}{2})^n(\frac{1}{2})^n =(\frac{1}{2})^(2n) =P(Z=0)$

But, I am not sure I have done it correctly or not. The answer in the text is $P(Z=n)$

Any help.?

userNoOne
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  • $X=Y$ can happen when $X$ and $Y$ are the same value; that need not be zero. – Graham Kemp May 13 '18 at 06:10
  • The simultaneous happening of X and Y can be represented by Z=0. Isn't it? Since, Z is the sum of X and Y. In no other cases, this can happen. – userNoOne May 13 '18 at 06:12

0 Answers0