Two random variables X and Y have a joint cumulative distribution function given by FXY(x, y) = 1/2 [u(x-2) + u(x-3)] {(1 exp(-y/2)) u(y), then the marginal probability density function fX(x) is given by

a.

1/2 delta(x-2) + 1/3 delta(x-3)

b.

delta(x-2) + delta(x-3)

c.

1/2 delta(x-2) + 1/2 delta(x-3)

d.

1/3 delta(x-2) + 1/3 delta(x-3)