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)

Question
Polynomial arithmetic
asked 2020-10-28
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 \(P(4 \leq x \leq 6)\)

Answers (1)

2020-10-29
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:
\(a. P(x \leq 6) = 1 - e^{-6/8} \approx 0.5276\)
\(b. P(x \leq 4) = 1 - e^{-4/8} \approx 0.3935\)
\(с. P(x \geq 6) = e^{-6/8} \approx 0.4724\)
\(d. P(4 \leq x \leq 6) = e^{-4/8} - e^{-6/8} \approx 0.1342\)
0

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