ee coup es and tr u sinu e individuals have een invited o n im estmert seminar a
ID: 3316163 • Letter: E
Question
ee coup es and tr u sinu e individuals have een invited o n im estmert seminar ar d have agreed to attend. Suppose he probabit, hat any par cular couple ur ind dua amves late rrh late. Assume thar dfferant couples and indviduals ars on tima or late indapandently of ane anothar. Let x-the number of paopla who arive late for the semina. 0.21 couple wil travu toge er 1n he same cle soe ther t people wil ve on time or e se both wil (a Determine the probability mass function ufX. Hint: label thu three couples #1 #2 and #3 and the two rdwiduals #4 and #2. Round your answers to our dearna places. 135012511 132991399 14865583 O3060131 7001591311 b) Obtain the aimulative distribution tuntion of X, :Round your answers to tour decimal paces.) 2 0530012 5 10972979 6 101249 1.02884 8 1 032753 lkE the runnulati." dktrih:tionfinction of X to calculate p(2 7). (Round your answer ta four necimal planes.)Explanation / Answer
P(X = 2)
= either one of couple comes late and no single comes late or no couples comes late and both singles come late
= 3 * 0.33 *(1-0.33)^4 + (1-0.33)^4 * 0.33*0.33
= 0.22144066866
b) cdf is P(X< = x)
P(X<=2) = P(X=0)+ P(X =1) +P(X = 2)
= 0.1350125 + 0.132997399 +0.22144066866
=0.489450
similarly other
P(X<= k) = P(X<= k-1 )+P(X =k)
c) P(2 <= X<= 7) = P(X<= 7) - P(X<=1)
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