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Q4. An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The CDF of X is given as follows:
F[x]=
0 x<2
0,2 2<=x<4
0,4 4<=x<=6
1 x>=6
Also let Y = Min [2X+1, 6]
Which one of the following is not true? Hint: Find the PMF of X first, then PMF of Y.
A) P[X = 4] = 0.2
B) P[Y > 4] = 1.0
C) P[Y > 14] = 0.0
D) P[Y ≤ 8.1 | Y ≥ 4.8] = 1.0
E) E[X] = 4.8
F) V[X] = 2.56
G) E[Y] = 5.8
H) V[Y] = 0.16
I) V[2Y+1] = V[2Y-1]
J) P[Y ≥ 6] = 0.
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