State conditions only

Questions that only ask to state, list, or write down the conditions/assumptions needed for a Poisson distribution to be valid, without requiring explanation or contextual application.

2 questions · Moderate -0.8

5.02i 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 modelling
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OCR MEI Further Statistics Major 2019 June Q2
9 marks Moderate -0.8
2 A special railway coach detects faults in the railway track before they become dangerous.
  1. Write down the conditions required for the numbers of faults in the track to be modelled by a Poisson distribution. You should now assume that these conditions do apply, and that the mean number of faults in a 5 km length of track is 1.6 .
  2. Find the probability that there are at least 2 faults in a randomly chosen 5 km length of track.
  3. Find the probability that there are at most 10 faults in a randomly chosen 25 km length of track.
  4. On a particular day the coach is used to check 10 randomly chosen 1 km lengths of track. Find the probability that exactly 1 fault, in total, is found.
Pre-U Pre-U 9795/2 2018 June Q2
Moderate -0.8
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 .