Consider the exponential probability density function: for x ≥ 0 Choose the correct formula for P...

Question

Question

Consider the exponential probability density function:

for x ≥ 0

Choose the correct formula for P (x ≤ x₀).

(1) P (x ≤ x₀) = 1 - e^(-x₀/3)

(2) P (x ≤ x₀) = 1 + e^(-x₀/3)

(3) P (x ≤ x₀) = 1 - (1/3)e^(-x₀/3)

(4) P (x ≤ x₀) = 1 + (1/3)e^(-x₀/3)
Find P (x ≤ 2). If required, round your answer to four decimal places.

P (x ≤ 2) =
Find P (x ≥ 3). If required, round your answer to four decimal places.

P (x ≥ 3) =
Find P (x ≤ 5). If required, round your answer to four decimal places.

P (x ≤ 5) =
Find P (2 ≤ x ≤ 5). If required, round your answer to four decimal places.

P (2 ≤ x ≤ 5) =

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Answer 1

Answer #1

(a) The exponential probability distribution is given by 1 − e^−λx

This gives the area under the probability distribution function

Hence, correct option is (1) P (x ≤ x₀) = 1 - e^(-x₀/3)

(b) P (x ≤ 2) = 1 - e^(-2/3) = 0.4866

(c) P (x ≥ 3) = 1 - P (x ≤ 3) = 1 - (1 - e^(-3/3)) = e^-1 = 0.3679

(d) P (x ≤ 5) = 1 - e^(-5/3) = 0.8111

(e) P (2 ≤ x ≤ 5) = (x ≤ 5) - (x ≤ 2) = (1 - e^(-5/3) ) - (1 - e^(-2/3) ) = 0.8111 - 0.4866 = 0.3245

Answer 2

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