1. Solve the following A. Strikes in a factory occur according to a Poisson process at a mean rate of 2 per year (we ass

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1 Solve The Following A Strikes In A Factory Occur According To A Poisson Process At A Mean Rate Of 2 Per Year We Ass 1 (165.59 KiB) Viewed 34 times

1. Solve the following A. Strikes in a factory occur according to a Poisson process at a mean rate of 2 per year (we assume a year to be exactly 52 weeks). (a) Find the probability that there is exactly one strike in the first 4 weeks and exactly 3 strikes in the subsequent 13 weeks. (b) What is the probability that at least 2 strikes occur in 13 weeks? (c) How many strikes are expected to occur in 2 years? B. Suppose a value is chosen “at random” in the interval [0,6]. In other words, x is an observed value of a random variable X • U(0,6). The random variable X divides the interval (0,6) into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P (Y>y) for any given y. (c) Find both the cdf and the pdf of Y. Can you tell the name of the distribution of Y?