On average, there are two bicycle thefts every ten square miles during the course of a month. What is the probability that there will no bicycle thefts in a ten square mile area next month? What is the probability that there will be at least one bicycle theft in a twenty square mile area?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
- On average, there are two bicycle thefts every ten square miles during the course of a month.
- What is the probability that there will no bicycle thefts in a ten square mile area next month?
- What is the probability that there will be at least one bicycle theft in a twenty square mile area?
a. Define the Random Variable,
X : Number of bicycle thefts in ten square miles next month
Average number of bicycle thefts = 2
This problem can be modelled as Poisson distribution.
So, X ~ Poisson(2)
PMF of X is given by,
P(X=x) =
To find the probability,
P(no cycle thefts)
= P(X=0)
= e-2 = 0.1353
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