Let X and Y be the random variables that count the number of heads and the number of tails that come up when two fair coins are flipped. Click and drag statements to show that X and Y are not independent. Therefore, X and Y are not independent. Therefore, X and Y are not independentHowever, for vi = 1 and 7 = 1. we have p.X-1 and Y-1) -- while p(X=1) y (X=1) = (1/2) : (1/2) = 1However, for r = 2 and 3 = 2. we have p(X= 2 and Y = 2) = 0 because X + Y must always be 2. while p(x = 2). (Y = 2)=6X) 16 = 2 1.1 44 X and Y are independent if p(.X = 1, and Y =")=(X=?:)p(Y = 13) for all real mumbers and r. X and Y are independent if p(X = 1 and Y = 1)) = P(X=ri)+ p(Y =r2) for all real numbers r2, and r2;.

Let X and Y be the random variables that count the number of heads and the number of tails that come up when two fair coins are flipped. Click and drag statements to show that X and Y are not independent. Therefore, X and Y are not independent .

Although there are lots of other ways to show

that they’re independent, it’s enough to show that

P ( XY ) = P ( X ) P ( Y ). First note that P ( X ) and

P ( Y ) are both 1. Next to compute P ( XY ). With

P ( XY ) = 1/4 * 0 + 1/2 * 1 + 1/4 * 0

= 1/2

therefore X and Y are not independent random variables

Learn more about the variables here:

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