Respuesta :
The solutions are;
The joint probability of y1 and y2 is [tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex] and F(1,0) = 1/3.
Given data;
Let y1 signify the number of contracts awarded to firm a and y2 the number of contracts assigned to firm b. Recall that each firm can receive 0, 1, or 2 contracts. Contracts for two construction tasks are randomly assigned to one or more of three firms, a, b, and c.
To find,
(a) The joint probability function for y₁ and y₂
Let y₁ denote the number of contracts assigned to firm A,
y₂ the number of contracts assigned to firm B
y₁
[tex]\left[\begin{array}{ccc}0&1&2\\\\\end{array}\right][/tex]
y₂
[tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex]
(b) Find F(1,0)
F(1,0) = p(y₁ ≤ 1, y₂ ≤ 0)
= p(0,0) + p(1,0)
= 1/9 + 2/9
= 1/3.
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