Pre-U Pre-U 9795/2 2018 June — Question 2

Exam BoardPre-U
ModulePre-U 9795/2 (Pre-U Further Mathematics Paper 2)
Year2018
SessionJune
TopicPoisson distribution
TypeState conditions only
DifficultyModerate -0.8 Part (i) asks for standard recall of Poisson conditions (independence and constant rate), which is textbook knowledge. Parts (ii) and (iii) involve routine Poisson calculations with scaling—standard Further Maths Statistics exercises requiring no novel insight, though (iii) requires solving for time which adds minor complexity.
Spec5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02l Poisson conditions: for modelling5.02n Sum of Poisson variables: is Poisson
2 Secret radio messages received under difficult conditions are subject to errors caused by random instantaneous breaks in transmission. The number of errors caused by breaks in transmission in a 10-minute period is denoted by \(B\).
  1. State two conditions, other than randomness, needed for a Poisson distribution to be a suitable model for \(B\). Assume now that \(B \sim \mathrm { Po } ( 5 )\).
  2. Calculate the probability that in a 15-minute period there are between 6 and 10 errors, inclusive, caused by random breaks in transmission. Secret radio messages are also subject to errors caused by mistakes made by the sender. The number of errors caused by mistakes made by the sender in a 10 -minute period, \(M\), has the independent distribution \(\operatorname { Po } ( 8 )\).
  3. Calculate the period of time, in seconds, for which the probability that a message contains no errors of either sort is 0.6 .
2 Secret radio messages received under difficult conditions are subject to errors caused by random instantaneous breaks in transmission. The number of errors caused by breaks in transmission in a 10-minute period is denoted by $B$.\\
(i) State two conditions, other than randomness, needed for a Poisson distribution to be a suitable model for $B$.

Assume now that $B \sim \mathrm { Po } ( 5 )$.\\
(ii) Calculate the probability that in a 15-minute period there are between 6 and 10 errors, inclusive, caused by random breaks in transmission.

Secret radio messages are also subject to errors caused by mistakes made by the sender. The number of errors caused by mistakes made by the sender in a 10 -minute period, $M$, has the independent distribution $\operatorname { Po } ( 8 )$.\\
(iii) Calculate the period of time, in seconds, for which the probability that a message contains no errors of either sort is 0.6 .

\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2018 Q2}}
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