Question

1. construct a probability distribution for the data and draw a histogram for the following:

a. a die is loaded in such a way that the probabilities of getting 1, 2, 3, 4, 5, and 6 are 1/2, 1/6, 1/12, 1/12, 1/12, and 1/12 respectively.
x
p(x)
b. a box contains 3 $1 bills, 2 $5 bills, 1 $10 bill, and 1 $20 bill.
x
p(x)

Explanation:

Step1: Calculate total number of bills for part b

Total number of bills \(n = 3 + 2+1 + 1=7\)

Step2: Calculate probabilities for part a

For \(X = 1\), \(P(X = 1)=\frac{1}{2}\)
For \(X = 2\), \(P(X = 2)=\frac{1}{6}\)
For \(X = 3\), \(P(X = 3)=\frac{1}{12}\)
For \(X = 4\), \(P(X = 4)=\frac{1}{12}\)
For \(X = 5\), \(P(X = 5)=\frac{1}{12}\)
For \(X = 6\), \(P(X = 6)=\frac{1}{12}\)

Step3: Calculate probabilities for part b

For \(X = 1\), \(P(X = 1)=\frac{3}{7}\)
For \(X = 5\), \(P(X = 5)=\frac{2}{7}\)
For \(X = 10\), \(P(X = 10)=\frac{1}{7}\)
For \(X = 20\), \(P(X = 20)=\frac{1}{7}\)

Answer:

Part a

\(X\)	\(P(X)\)
\(2\)	\(\frac{1}{6}\)
\(3\)	\(\frac{1}{12}\)
\(4\)	\(\frac{1}{12}\)
\(5\)	\(\frac{1}{12}\)
\(6\)	\(\frac{1}{12}\)

Part b

\(X\)	\(P(X)\)
\(5\)	\(\frac{2}{7}\)
\(10\)	\(\frac{1}{7}\)
\(20\)	\(\frac{1}{7}\)