Three couples and two single Indivduals have been Invited to an nvestment semina

Question

Three couples and two single Indivduals have been Invited to an nvestment seminar and have agreed to attend. Suppose the probabllty that any particular couple or Indlvidual arrives late ls 0.43 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X- the number of people who arrive late for the seminar (a) Determine the probability mas5 function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your an5wers to tour decimal places.) or Px) (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) Fx) Use the cumulative distribution function of X to calculate P(2 s X s). (Round your answer to four decimal places.)

Explanation / Answer

from above" P(X=x)=P(a couples late and x-2a individuals late)

hence

a)

b)

P(2<=X<=6)=0.7954

x P(x) 0 0.0602 1 0.0908 2 0.1704 3 0.2055 4 0.1802 5 0.1550 6 0.0843 7 0.0390 8 0.0147

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