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 <em>Xi</em> is defined as follows:
<em>Xi</em> = 1; if the ith ball is white
<em>Xi</em> = 0; otherwise.
Then <em>X</em>₁ = the 1st ball is white and <em>X</em>₂ = 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:
![P(X_{1} = 0, X_{2}= 0)=\frac{8}{13} \times\frac{7}{12}=\frac{14}{39}](https://tex.z-dn.net/?f=P%28X_%7B1%7D%20%3D%200%2C%20X_%7B2%7D%3D%200%29%3D%5Cfrac%7B8%7D%7B13%7D%20%5Ctimes%5Cfrac%7B7%7D%7B12%7D%3D%5Cfrac%7B14%7D%7B39%7D)
![P(X_{1} = 0, X_{2}= 1)=\frac{8}{13} \times\frac{5}{12}=\frac{10}{39}](https://tex.z-dn.net/?f=P%28X_%7B1%7D%20%3D%200%2C%20X_%7B2%7D%3D%201%29%3D%5Cfrac%7B8%7D%7B13%7D%20%5Ctimes%5Cfrac%7B5%7D%7B12%7D%3D%5Cfrac%7B10%7D%7B39%7D)
![P(X_{1} = 1, X_{2}= 0)=\frac{5}{13} \times\frac{8}{12}=\frac{10}{39}](https://tex.z-dn.net/?f=P%28X_%7B1%7D%20%3D%201%2C%20X_%7B2%7D%3D%200%29%3D%5Cfrac%7B5%7D%7B13%7D%20%5Ctimes%5Cfrac%7B8%7D%7B12%7D%3D%5Cfrac%7B10%7D%7B39%7D)
![P(X_{1} = 1, X_{2}= 1)=\frac{5}{13} \times\frac{4}{12}=\frac{5}{39}](https://tex.z-dn.net/?f=P%28X_%7B1%7D%20%3D%201%2C%20X_%7B2%7D%3D%201%29%3D%5Cfrac%7B5%7D%7B13%7D%20%5Ctimes%5Cfrac%7B4%7D%7B12%7D%3D%5Cfrac%7B5%7D%7B39%7D)
The joint probability mass function table is provided below.