Let's calculate the following exponential probability density function. f(x) = frac{1}{8} e^{x/8} for x geq 0 a.Find P(x leq 4) b.Find P(x leq 6) с.Find P(x geq 6) d.Find P(4 leq x leq 6)

Let's calculate the following exponential probability density function.
$$f(x) = \frac{1}{8} e^{x/8} for x \geq 0$$
a.Find $$P(x \leq 4)$$
b.Find $$P(x \leq 6)$$
с.Find $$P(x \geq 6)$$
d.Find $$P(4 \leq x \leq 6)$$

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Clelioo
Given: $$f(x) = \frac{1}{8} e^{-x/8}\ for\ x \geq 0 \mu = 8$$
Formula exponential probability:
$$P(x \leq a) = 1 - e^{-a/ \mu}$$
$$P(a < x < b) = e^{-a/ \mu} - e^{-b/ \mu}$$
Detetmine the probabilities:
$$a. P(x \leq 6) = 1 - e^{-6/8} \approx 0.5276$$
$$b. P(x \leq 4) = 1 - e^{-4/8} \approx 0.3935$$
$$с. P(x \geq 6) = e^{-6/8} \approx 0.4724$$
$$d. P(4 \leq x \leq 6) = e^{-4/8} - e^{-6/8} \approx 0.1342$$