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12 April, 19:03

Consider the following exponential probability density function. f (x) = 1 5 e-x/5 for x ≥ 0 (a) Write the formula for P (x ≤ x0). (b) Find P (x ≤ 4). (Round your answer to four decimal places.) (c) Find P (x ≥ 5). (Round your answer to four decimal places.) (d) Find P (x ≤ 6). (Round your answer to four decimal places.) (e) Find P (4 ≤ x ≤ 6). (Round your answer to four decimal places.)

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  1. 12 April, 19:20
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    Question:

    Consider the following exponential probability density function.

    f (x) = 1/5e^ (-x/5) for x ≥ 0

    (a) Write the formula for P (x ≤ x0). (b) Find P (x ≤ 4). (Round your answer to four decimal places.) (c) Find P (x ≥ 5). (Round your answer to four decimal places.) (d) Find P (x ≤ 6). (Round your answer to four decimal places.) (e) Find P (4 ≤ x ≤ 6). (Round your answer to four decimal places.)

    Answer:

    (a) P (x ≤ x0) = 1 - e^ (-x0/5)

    (b) P (x ≤ 4) = 0.5506

    (c) P (x ≥ 5) = 0.3678

    (d) P (x ≤ 6) = 0.6988

    (e) P (4 ≤ x ≤ 6) = 0.1482

    Step-by-step explanation:

    The standard form of the exponential probability density function is given by

    f (x) = 1/μe^ (-x/μ)

    Where μ is the mean, for the given problem μ = 5

    (a) Write the formula for P (x ≤ x0)

    P (x ≤ x0) = 1 - e^ (-x0/5)

    (b) Find P (x ≤ 4)

    P (x ≤ 4) = 1 - e^ (-4/5)

    P (x ≤ 4) = 1 - 0.4493

    P (x ≤ 4) = 0.5506

    (c) Find P (x ≥ 5)

    P (x ≥ 5) = e^ (-5/5)

    P (x ≥ 5) = 0.3678

    (d) Find P (x ≤ 6)

    P (x ≤ 6) = 1 - e^ (-6/5)

    P (x ≤ 6) = 1 - 0.3011

    P (x ≤ 6) = 0.6988

    (e) Find P (4 ≤ x ≤ 6)

    P (4 ≤ x ≤ 6) = e^ (-4/5) - e^ (-6/5)

    P (4 ≤ x ≤ 6) = 0.4493 - 0.3011

    P (4 ≤ x ≤ 6) = 0.1482
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