Consider the following exponential probability density function. $f(x) = frac{1}{2}e^{-frac{x}{2}}$ for $x ge 0$ a. Which of the following is the formula for $P(x le x_0)$? 1 $P(x le x_0) = e^{-frac{x_0}{2}}$ 2 $P(x le x_0) = 1 - e^{-frac{x_0}{2}}$ 3 $P(x le x_0) = 1 - e^{-x_0}$ Formula #2 b.Find $P(x le 1)$ (to 4 decimals). 0.3935 c. Find $P(x ge 4)$ (to 4 decimals). 0.8647 d.Find $P(x le 5)$ (to 4 decimals). 0.9179 e.Find $P(1 le x le 5)$ (to 4 decimals). 0.5245
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Step 1:** Calculate the cumulative distribution function (CDF) for the exponential density function given: \[ F(e) = \int_{0}^{e} 1e^{-2e/20} de \] \[ F(e) = -\frac{10}{e}e^{-2e/20} \Big|_{0}^{e} \] \[ F(e) = -10e^{-e/10} + 10 \] ** Show more…
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