Let qe (0,1). A machine produces N devices during its life-time, where P (N = = c”, n >1 P(N = 0) = 1 -c Žq". n=1 Each d

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Let Qe 0 1 A Machine Produces N Devices During Its Life Time Where P N C N 1 P N 0 1 C Zq N 1 Each D 1 (84.6 KiB) Viewed 73 times

Let qe (0,1). A machine produces N devices during its life-time, where P (N = = c”, n >1 P(N = 0) = 1 -c Žq". n=1 Each device the machine produces is equally likely to be faulty or non-faulty, independently of the other devices. (a) (5 marks) Show that the probability that the machine produces j faulty devices is 2cq (2 — q)3+1 for j > 1. 3 4 CONTENTS You may use without proof that for x € (0,1), k=0 m! k(k – 1) ... (k – m +1)xk (1 – x)m+1: (b) [4 marks] Given that the machine has produced at least 1 faulty device over its lifetime, what is the probability that the machine will produce at least 2 faulty devices.