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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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