The problem here is a Joint Probability Distribution exercise. See the answers and explanation below.
What is Joint Probability Distribution?
Joint Probability Distribution can be simply described as the likelihood of two events (variables) occurring at the same time.
These two events are commonly referred to as event A and event B, and their formal names are: p (A and B).
What is the solution to the questions?
A - The likelihood that each line has exactly one customer: The probability relates to the associated row and column.
X₁ = 1 and X₂ = 1
P (X₁ = 1, X₂ =1) = 0.15
B - The sum of the diagonal elements of the joint pmf indicates the likelihood that the amount of clients in both lines is the same:
P(X₁ = X₂) =) p(0,0) + p (1,1) + p(2, 2) + p(3,3
= 0.08 + 0.15 + 0.10 + 0.07
= 0.4
Hence,
[tex]P(X_{1} = X_{2}) = 0.40[/tex]
C - Let A represent the situation in which there are at least two more clients than the other line: The following are examples of variable combinations:
X₂ =0 ; X₁ = 2,3, 4
X₂ =1 ; X₁ = 3, 4
X₂ =2 ; X₁ = 0, 4
X₂ =3 ; X₁ = 0, 1
The probability is thus computed as follows:
P (A) = p(1, 3) + p (2,2) + p(2, 3) + p(3,1) + p(3,2) + p(3,3) + p(4,0) + p(4,1) + p(4,2) + p(4,3)
= 0.04 + 0.10 +0.06 + 0.03 + 0.04+ 0.07 + 0.00 + 0.01 + 0.05 + 0.06
= 0.46
Hence [tex]P (A) = 0.46[/tex]
Learn more about Joint Probability Distribution at:
https://brainly.com/question/6003812
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