Question

Let X be defined as follows. Let Y1, Y2 ∼ Ber(1/2) be independent and {0, 1} valued and let Z ∼ U[0, 1], independent from the rest, then

X = (Y1 if Y2 = 0

Z if Y2 = 1.

Express the CDF of X in terms of that for Y1 and Z.

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