Don\'t get b and c , thanks An article suggests that a Poisson process can be us

Question

Don't get b and c , thanks

An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year (a) How many loads can be expected to occur during a 2-year period? loads (b) What is the probability that more than six loads occur during a 2-year period? (Round your answer to three decimal places.) 001 (c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.1? (Round your answer to four decimal places.) 60195

Explanation / Answer

b) mean = 0.4 * 2 = 0.8 per 2 year

P(X = x) = e-0.8 * 0.8x / x!

P(X > 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))

              = 1 - (e-0.8 * 0.80 / 0! + e-0.8 * 0.81 / 1! + e-0.8 * 0.82 / 2! + e-0.8 * 0.83 / 3! + e-0.8 * 0.84 / 4! + e-0.8 * 0.85 / 5! + e-0.8 * 0.86 / 6! )

             = 1 - 1

             = 0

c) P(X = 0) < 0.1

or, e-0.4*n * (0.4*n)0 / 0! < 0.1

or, e-0.4*n < 0.1

or, 0.4*n > -ln(0.1)

or, n > 5.7565 years

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