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Unformatted text preview: cise the calculation of P( X ≤ 1) was found with BINOMDIST(1, 6, 0.15, 1) = 0.7765 Therefore, the answer is: P(X > 1) = 1 − P( X ≤ 1) = 1 − 0.7765 = 0.2235 Note: an important assumption ofthe binomial distribution is independent trials. 22 Chapter 5 Chapter 5.7 Jointly Distributed Random Variables Economic relationships between variables are of interest. Let X and Y be a pair of discrete random variables such that: X has numerical outcomes x, and Y has numerical outcomes y. The joint probability function is: PX , Y (x , y) = P(X = x and Y = y ) for all pairs (x, y) A joint probability function has the properties: • 0 ≤ PX , Y (x , y ) ≤ 1 • for all pairs (x, y) ∑ ∑ PX , Y (x , y ) = 1 xy 23 Chapter 5 The probability function of X is obtained by summing the joint probabilities: PX (x) = ∑ PX , Y (x , y ) for all possible values of x. y ↑ summation over all possible values of y. This is called the marginal probability function of X. Similarily, the marginal probability function of Y is constructed as: PY (y ) = ∑ PX , Y (x , y ) for all possible values of y. x The conditional probability function of Y given that X = x is: PY|X (y x) = PX , Y (x , y )
PX (x) for all possible values of y. Similarily, the conditional probability function of X given that Y = y is: PX|Y (x y ) = PX , Y (x , y )
PY (y ) for all possible values of x. For the conditional probab...
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