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 = 0.1. (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

From given data = M = 0.1 → using poisson distribution. The probability mass function (PMF) = fxcx) poission distribution fxcx) = Şeol.co.1) 22! x=0,1,2... ; Otherwise a-) The probability that a disk hey exactly one missing pulse is P(x = = eº to.. ū =0.090) b.) The probability that adisk hay at least two missing pulses 's PCX3,2)= 1- P(x2) PLX22) = 1-Pex=0)+PCX=1)] PCX72) = 1-1 20 20.10 éal, 0! Tu P(X72) = 1-(0.905 +0.090] PCX32) =10.005) C.) If twoo disks are independently selected, X, = Number of missing pulse for 1st disk. Xo = Number of missing pulse for and disk. The probability that neither contains a missing pulse is P[ x,-0, Xq=0] = P(x=0]. P[x207 - 0.819