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.
(type integers or decimals. do not round.)

Explanation:

Step1: Calculate the total number of members

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

Step2: Calculate \(P(Y = 3)\)

Using the formula \(P(Y=y)=\frac{f}{N}\), for \(y = 3\), \(f = 1\) and \(N = 10\). So \(P(Y = 3)=\frac{1}{10}=0.1\)

Step3: Calculate \(P(Y = 4)\)

For \(y = 4\), \(f = 1\) and \(N = 10\). So \(P(Y = 4)=\frac{1}{10}=0.1\)

Step4: Calculate \(P(Y = 5)\)

For \(y = 5\), \(f = 6\) and \(N = 10\). So \(P(Y = 5)=\frac{6}{10}=0.6\)

Step5: Calculate \(P(Y = 6)\)

For \(y = 6\), \(f = 2\) and \(N = 10\). So \(P(Y = 6)=\frac{2}{10}=0.2\)

Answer:

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