A fair coin is tossed three times, let X be the number of cases in which the HEAD is obtained, and Y be the absolute value of difference between the number of HEAD and the number of TAIL. Seek the distribution law (that is, the PMF) of random variables (X,Y). (Hint: First consider the discrete value range of X and Y (0 to 3 each), and the Bernoulli trial, and list all the PMF’s)
2026-04-22 21:23:37.1776893017
Bernoulli Distribution (PMF) of random variables X,Y
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Hint:
$\mathbf{Y}=\left|\mathbf{X}-\left(3-\mathbf{X}\right)\right|=\left|2\mathbf{X}-3\right|$ so $\mathbf{X}$ determines $\mathbf{Y}$.