By Petr Mandl
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5. 0192. ✷ More generally, if n discrete random variables X1 , . . , Xn are independent, it follows that P(X1 = x1 , X2 = x2 , . . , Xn = xn ) = P(X1 = x1 )P(X2 = x2 ) . . 24) for any sequence x1 , . . , xn of observed values. For independent continuous random variables X1 , X2 , . . , Xn , we must use probabilities instead of intervals. If h1 , . . , hn are small positive numbers, then12 P(X1 ∈ [x1 , x1 + h1 ], X2 = [x2 , x2 + h2 ], . . , Xn = [xn , xn + hn ]) ≈ fX1 (x1 )fX2 (x2 ) . . fXn (xn )h1 h2 .
No genetic model needs to be specified, and this is an advantage for complex diseases such as inheritable diabetes and psychiatric disorders. 3 Linear regression Depending on the causal connections between two variables, X and Y , their true relationship may be linear or nonlinear. In any case, a linear model can always be used as a first approximation to the true pattern of association. e. 7) ✕ where ✡ is the y-intercept, is the slope of the line, the regression coefficient, and e is the residual error.
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