Question

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter u = 0.5. (Round your answers to three decimal places.) (a) What is the probability that a disk has exactly one missing pulse? (b) What is the probability that a disk has at least two missing pulses? (c) If two disks are independently selected, what is the probability that neither contains a missing pulse? You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Sol eiveny Considnnotny than Seding ovilo a Computey disk and a Certifes, with poisson t through distrikution, avemere =0.5 X~ poisson (k0.5) According hy distri bution i to the poisson missing pele (a)Probabiby tha disk has eracy one e., we need find PCx=1) -0.5 (0.s) e o.5 Co.5) 0. 303 probabilky that a disk has exady ene = 0.303

(ro babi that disk has atleast to missing f.e., tne we meed t fnd P2) - Fx2) -(PCK-c)t poxi)] -e) 0.5)0 0-5) o! !! 1-0.6065 + 0.30 32 |- [o.9097] 0. 0103 o.090 P(X22)0.09 Probabibly that a drk has vatleast ta P2)0.090 miking pales is (e pobabilthat neithen Contains paulkes t means, it Contains ro pules So, it follor,

i.e. P(neithe Contains mSony PCxo)PCX0) Pulse 2- o! Co.6065) 1 0.36784 0.368 : p (nerther Contains pulel