Answer:
The joint probability mass function table is provided below.
Step-by-step explanation:
The experiment consist of drawing 3 balls from an urn containing 5 white and 8 red balls.
The random variable Xi is defined as follows:
Xi = 1; if the ith ball is white
Xi = 0; otherwise.
Then X₁ = the 1st ball is white and X₂ = the 2nd ball is white.
The sample space is as follows:
S = {(X₁ = 0, X₂ = 0), (X₁ = 0, X₂ = 1), (X₁ = 1, X₂ = 0), (X₁ = 1, X₂ = 1)}
Compute the probability of each event in the sample space as follows:
[tex]P(X_{1} = 0, X_{2}= 0)=\frac{8}{13} \times\frac{7}{12}=\frac{14}{39}[/tex]
[tex]P(X_{1} = 0, X_{2}= 1)=\frac{8}{13} \times\frac{5}{12}=\frac{10}{39}[/tex]
[tex]P(X_{1} = 1, X_{2}= 0)=\frac{5}{13} \times\frac{8}{12}=\frac{10}{39}[/tex]
[tex]P(X_{1} = 1, X_{2}= 1)=\frac{5}{13} \times\frac{4}{12}=\frac{5}{39}[/tex]
The joint probability mass function table is provided below.
