Question

a certain hurricane database extends back to 1851, recording among other data the number of major hurricanes (measuring at least a category 3) striking a certain region per year. the following table provides a probability - distribution for the number of major hurricanes, y, for a randomly selected year between 1851 and 2012. complete parts (a) through (f) below.

y	p(y = y)	y	p(y = y)
1	0.281	6	0.027
2	0.264	7	0.008
3	0.078	8	0.002
4	0.037

a. use random - variable notation to represent the event that the year had at least one major hurricane. select the correct choice below and fill in the answer box within your choice.
a. p( )
b. (y≥1)
b. use random - variable notation to represent the event that the year had exactly eight major hurricanes. select the correct choice below and fill in the answer box within your choice.
a. (y = 8)
b. p( )
c. use random - variable notation to represent the event that the year had between 2 and 4 major hurricanes, inclusive. select the correct choice below and fill in the answer box within your choice.
a. ( )
b. p( )

Explanation:

Step1: Recall random - variable notation

In probability, if \(Y\) is a random variable representing the number of major hurricanes, the event of at least one major hurricane means \(Y\) is greater than or equal to 1, written as \(Y\geq1\).

Step2: For exactly eight major hurricanes

If \(Y\) is the random variable, the event of exactly eight major hurricanes is written as \(Y = 8\).

Step3: For between 2 and 4 major hurricanes inclusive

If \(Y\) is the random variable, the event of having between 2 and 4 major hurricanes inclusive is written as \(2\leq Y\leq4\).

Answer:

a. \(Y\geq1\)
b. \(Y = 8\)
c. \(2\leq Y\leq4\)