3.8 A random variable has a CDF given by $F_X(x) = (1-e^{-x})u(x)$. (a) Find Pr($X > 3$). (b) Find Pr($X < 5|X > 3$). (c) Find Pr($X > 6|X > 3$). (d) Find Pr($|X - 5| < 4||X - 6| > 2$).
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The unit step function $u(x)$ is defined as: $u(x) = 1$ for $x \ge 0$ $u(x) = 0$ for $x < 0$ This means that $F_X(x) = 0$ for $x < 0$ and $F_X(x) = 1 - e^{-x}$ for $x \ge 0$. This is the CDF of an exponential distribution with parameter $\lambda = 1$. We know Show more…
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