# iPad 8:04 PM Problem 8. Let X be defined as follows. Let Y.Y2 ~ Ber( ) be independent and 0,1 valued and let Z ~U[0, 1], independent from the rest, then Express the CDF of X in terms of that for Yi and Z.

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.