document.write( "Question 1011722: 14. If calls to your cell phone are a Poisson process with a constant rate l=2 calls per hour, what’s the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? How many phone calls do you expect to get during the movie? \n" ); document.write( "
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\n" ); document.write( "Question:
\n" ); document.write( "If calls to your cell phone are a Poisson process with a constant rate l=2 calls per hour, what’s the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? How many phone calls do you expect to get during the movie?
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\n" ); document.write( "Solution:
\n" ); document.write( "Given Poisson processes.
\n" ); document.write( "mean=λ=2 (per hour)
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\n" ); document.write( "For a duration of 1.5 hours, mean = 3
\n" ); document.write( "P(not ring during 1.5 hours)
\n" ); document.write( "=P(0;3)=0.049787 (from tables of Poisson distribution)
\n" ); document.write( "Expected number of calls = mean = 3\r
\n" ); document.write( "\n" ); document.write( "Reference:
\n" ); document.write( "Poisson tables
\n" ); document.write( "http://www.dtic.upf.edu/~jblat/material/pipe/poisson_distribution.pdf
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