Example 18.4-1 0 % follows an exponential distribution. Find the following: 2 Babies are born in a large city at the rate of one birth every 12 minutes. The time between births . 365 X22 (Dodire 6) The probability that no births will occur during1 day) - Pen (1) (c) The probability of issuing 50 birth certificates in 3 hours, given that 40 certificates were issued during the first 2 hours of the 3-hr period. (a). The average number of births per year. 5X24 - 122 2 (X=120 + /200385 /teak Poolt e-120 The birth rate per day is computed as 15% 24 x 60 = = 120 births/day 12 Thus, the number of births per year in the state is at & At = 120 X 365 = 43,800 births/year The probability of no births during 1 day is (120 x 1)e-120x1 Po(1) 0 0! DO Another way to compute the same probability is to note that no birth in any one day is equiva- lent to saying that the time between successive births exceeds one day, We can thus use the exponential distribution to compute the desired probability as no little to P{t > 1} = e-120 = 0 (ros 26-120 Because the distribution of the number of births is Poisson, the probability of issuing 50 certificates in 3 hours, given that 40 certificates were issued during the first 2 hours, is equivalent to having 10(= 50 40) births in one (=3 - 2) hr--that is, 50P 3706. X P10(1) .01813 400) and att 10! lopol 150 l = 0 e-xt 1) "0e-5x1 the 18-20. Prove that the mean and standard deviation of the *18-21. In Example 18.4-1, suppose that the clerk who enters the information from birth certificates into the computer normally waits until at least 6 certificates have accumulated. Find the probability that the clerk will be entering a new batch every hour. an art collector travels to art auctions once a month on the average. Each trip nne purchase. The time between trips is exponentially 18.22