Question

a variable y of a finite population has the frequency distribution shown in the table. suppose a member is selected at random from the population and let y denote the value of the variable y for the member obtained. complete parts (a) through (d) below.

a. determine the probability distribution of the random variable y.

b. use random - variable notation to describe the events that y takes on the value 5, a value less than 5, and a value of at least 5.

the event that y takes on the value 5 can be represented as {}

Explanation:

Step 1: Calculate the total number of members

The total number of members \(n = 1+1 + 6+2=10\)

Step 2: Determine the probability distribution

The probability \(P(Y = y)\) is calculated as \(P(Y=y)=\frac{f}{n}\)

• For \(y = 3\), \(P(Y = 3)=\frac{1}{10}=0.1\)
• For \(y = 4\), \(P(Y = 4)=\frac{1}{10}=0.1\)
• For \(y = 5\), \(P(Y = 5)=\frac{6}{10}=0.6\)
• For \(y = 6\), \(P(Y = 6)=\frac{2}{10}=0.2\)

Answer:

The probability distribution of the random variable \(Y\) is:

\(y\)	\(P(Y = y)\)
\(4\)	\(0.1\)
\(5\)	\(0.6\)
\(6\)	\(0.2\)