Question

Solve problems using Rstudio. Show evidence that they used the program by putting screen shots of the results.

In a certain cruise, 3 traffic accidents occur, on average, each month. Answer the following:

a. Identifies the random process
b. Defines a variable
c. Associate the random variable with a distribution and its parameters

Solve the following questions using Rstudio:

d. Find the probability that exactly 4 accidents will occur in a 2-month period
e. Find the probability that at least 20 accidents will occur in a 6-month period
f. Find the probability that in a 1-month period they will occur at most 9 accidents.

Answer 1

a) here this follows poisson process, since events are independent from one interval to other and average number is fixed

b)

here X is number of accidents per month which follows poisson distribution with parameter λ =3

c)

this is Poisson distribution with parameter λt where λ =3 anf t are number of months

d)probabiltiy=0.1339

below is R code:L

e)

f)