Continuous random variable (stats)

  1. The probability density function of the time customers arrive at a terminal (in minutes after 8:00 A.M) is
    f(x)= (e^(-x/10))/10 for 0 < x

    c) Determine the probability that:

    two or more customers arrive before 8:40 A.M among five that arrive at the terminal. Assume arrivals are independent

    my logic is the following:

    Probability= 1-Probability 0 or 1 customers arrive before 8:40 A.M

    the answer is the following:

    P(X1>40)+ P(X1<40 and X2>40)= e-4+(1- e-4) e-4= 0.0363

    from what is written above, it seems to be the probability that no one arrives before 8:40 P(X1>40) and the probability that one arrives before 8:40 (X1<40) and another arrives after 8:40 (X2>40).

    i tihnk i just need some help on understanding why X2 is brought in.

  2. jcsd
  3. Your logic is correct. But the solution is wrong.

    Let p=P(a customer arrives at the terminal before 08:40)=P(X<40)=1-e^(-4)

    Then, P(0 or 1 customers arrive at the terminal before 08:40) = (1-p)^5 + nchoosek(5, 1)*p*(1-p)^4 = 5.5255*10^(-7) (approximately zero).

    Hence, P(2 or more customers arrive at the terminal before 08:40) = 1-5.5255*10^(-7) (approximately 1)
    Last edited: Jun 8, 2011
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