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Extra resources for A stochastic model for extinction and recurrence of epidemics estimation and inference for measles o

Example text

M. The train is, on average, a minute late and has a standard deviation of 4 minutes. The bus always leaves on time but is, on average, it minutes late with a standard deviation of 2 minutes. Find the probability for the man to be late for work. m. and the time for his journey has mean value 13 minutes with a standard deviation of 3 minutes. Find the probability that (i) both the man and his employer are late for work; and (ii) the employer arrives before the employee. All separate parts of the journeys may be assumed to have a normal distribution.

Initially. the single (W) and (B) balls are in the proportions Po and qo (Po + qo = 1), whilst the paired balls (WW), (WB), (BB) have the proportions roo 2so, to respectively (/'0+2so+to = 1). 20 EXERCISES IN PROBABILITY AND STATISTICS All the paired balls undergo a simultaneous disjunction, after which they are equally likely either to combine randomly with the original single balls only to form new pairs of the three types, or to remain single. This second population of paired and single balls repeats the process of separation and combination to form a third population, and this continues indefinitely.

Hence deduce that t (z+k-1)(r-1) = ~[(n+k)(r)-(k-l)(r)], z=o r and. in particular, fOI k r-l, = L (Z+k_l)(k) = (+k)(k+1) 11 . 'C x(x+l)y2 = l1(n+2)(n 2 -1)(1011 2 +411-3)/180. 2 Continuous random variables I A continuous random variable X has, for X = x, the probability density function k(l-x) defined in the unit interval (0 ~ X ~ 1). Determine the constant k and then find the mean, median and variance of the population. 2 A continuous random variable X defined over the range (0 ~ X < 00) has, for X = x, the distribution function (l_e- tx2).

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