Ship collisions in the houston ship channel are rare. suppose the number of collisions are poisson distributed, with a mean of 1.2 collisions every four months. appendix a statistical tables (round your answers to 4 decimal places.) a. what is the probability of having no collisions occur over a four-month period? b. what is the probability of having exactly two collisions in a two-month period? c. what is the probability of having one or fewer collisions in a six-month period?

  c)

Step-by-step explanation:

Rate of collision,

1.2 collisions every 4 months

or,

= 0.3 collisions per  month

So, the Poisson distribution for the random variable no. of collisions per month (X) is given by,

          P(X =x) =

                                                           for x ∈ N ∪ {0}

                       =  0 otherwise --------------------------------------(1)

here, collision / month

No collision over a 4 month period means no collision per month or X =0

Putting X = 0 in (1) we get,

         P(X = 0) =

                      ------------------------------------(2)

Now, since we are calculating  this for 4 months,

so, P(No collision in 4 month period)

     =

       -----------------------------------------------------------(3)

2 collision in 2 month period means 1 collision per month or X =1

Putting X =1 in (1) we get,

           P(X =1) =

                      ------------------------------------(4)

Now, since we are calculating this for 2 months, so ,

P(2 collisions in 2 month period)

                =

                -----------------------------------------(5)

1 collision in 6 months period means

                                collision per month

Now, P(1 collision in 6 months period)

= P( X = 1/6]  (which is to be estimated)

=

= \frac {0.7408182207 \times 5 + 0.2222454662 \times 1}{6}[/tex]

-------------------------------------------(6)

So,

P(1  collision in 6 month period)

  =  

    ------------------------------------------------(7)

So,

P(No collision in 6 months period)

  =

    ---------------------------------(8)

so,

P(1 or fewer collision in 6 months period)

= (8) + (7 ) = 0.0785267444 +0.1652988882

---------------------------------------------(9)          

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