Joint PMF of Two Coins
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Flip a fair coin twice, i.e., {HH;HT;TH;TT}.
Let X and Y be two random variables by
X(HH) = X(HT) = 2; X(TH) = X(TT) = 1;
Y (HH) =Y (TH) = 1; Y (HT) =Y(TT) = -1:
(a) Plot the joint pmf and joint cdf for X and Y .
(b) Are X and Y independent? Uncorrelated?
(c) Define Z = XY . Plot the joint pmf and joint cdf for X and Z.
(d) Are X and Z uncorrelated? Independent?
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Solution Summary
The solution gives detailed steps on finding the joint pmf after rolling two coins and deciding independence of two variables.
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(a) Plot the joint pmf and joint cdf for X and Y .
The joint pmf for X and Y is
H T
H X=2 Y=1 X=2 Y=-1
T X=1 Y=1 X=1 Y=-1
See attachment for graph.
(b) Are X and Y ...
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