The number of wrongly dialed phone calls you receive can be modeled as a Poisson process with the rate of one per month. For simplicity, ass

Question

The number of wrongly dialed phone calls you receive can be modeled as a Poisson process with the rate of one per month. For simplicity, assume there are four weeks in one month.

a. Find the probability that it will take between two and three weeks to get the first wrongly dialed phone call.
b. Suppose that you have not received a wrongly dialed phone call for two weeks. Find the expected value and variance of the additional time until the next wrongly dialed phone call.

in progress 0
Diễm Kiều 4 years 2021-08-29T00:23:41+00:00 1 Answers 29 views 0

Answers ( )

  1. King
    0
    2021-08-29T00:25:01+00:00
    Reply

    Answer:

    Part a: P (14/30<x<21/30) = 0.1304

    Partb:  Expected value= Variance=  0.866

    Step-by-step explanation:

    The poisson distribution is given by

    P(x)= μˣ . e^ -u/ x!

    In this question

    x= 1

    n= 30

    μ= 1/30

    P(x)= μˣ . e^ -u/ x!

    = 0.333. e⁻¹/³⁰/1!

    = 0.33*0.967/1

    = 0.32208

    For 2 weeks

    x= 14

    n= 30

    μ= 14/30

    P(x)= μˣ . e^ -u/ x!

    = 0.467. e⁻¹⁴/³⁰/14!

    = 0.467*0.627/14!

    = 0.29285/14!

    =3.359*e⁻¹²

    = 0.0139

    For 3 weeks

    x= 21

    n= 30

    μ= 21/30

    P(x)= μˣ . e^ -u/ x!

    = 0.7* e⁻²¹/³⁰/21!

    = 0.7*0.4965/21!

    = 0.3476/21!

    =6.8037*e⁻²¹

    = 0.11648

    Part a:

    P (14/30<x<21/30) = P (x= 14/30) + P (x=21/30)

    (0.0139 +0.11648) =0.1304

    Part b:

    Probability of Not receiving the call for two weeks =  1-  P (x= 14/30)=0.9861

    The mean and the variance of the Poisson distribution are equal to μ

    For x= 14

    Expected value  not getting wrongly dialed phone call in 2 week =  μ= 1-14/30 = 1-0.467= 0.533

    Variance of  not getting wrongly dialed phone call in 2 week=  μ=1- 14/30= 1-0.467= 0.533

    Expected  value of the additional time until the next wrongly dialed phone call

    Expected value not getting wrongly dialed phone call in 2 weeks + Expected value of next wrongly dialed phone call in a month

    = 0.533+0.33=0.866

    Variance of the additional time until the next wrongly dialed phone call

    = Expected  value of the additional time until the next wrongly dialed phone call =0.866

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )