Consider the following exponential probability density function.\\ $\frac{1}{2}e^{-x/2}$ for $x \ge 0$\ If needed, round your answer to four decimal digits.\ (a) Choose the correct formula for $P(x \le x_0)$.\ (i) $P(x \le x_0) = 1 + e^{x_0/2}$ (ii) $P(x \le x_0) = 1 - e^{x_0/2}$ \ (iii) $P(x \le x_0) = 1 + e^{-x_0/2}$ (iv) $P(x \le x_0) = 1 - e^{-x_0/2}$ \ Option (iv)\ (b) Find $P(x \le 2)$.\ .6321\ (c) Find $P(x \ge 3)$.\ (d) Find $P(x \le 5)$.\ .9179\ (e) Find $P(2 \le x \le 5)$.\ .2858
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Step 1: The correct formula for $P(x \le x_0)$ is $P(x \le x_0) = 1 - e^{-x_0/2}$. Show more…
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