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The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
The letter may be followed by a subscript: a number (as in x 2), another variable (x i), a word or abbreviation of a word (x total) or a mathematical expression (x 2i + 1). Under the influence of computer science , some variable names in pure mathematics consist of several letters and digits.
In words: the variance of Y is the sum of the expected conditional variance of Y given X and the variance of the conditional expectation of Y given X. The first term captures the variation left after "using X to predict Y", while the second term captures the variation due to the mean of the prediction of Y due to the randomness of X.
This implies that in a weighted sum of variables, the variable with the largest weight will have a disproportionally large weight in the variance of the total. For example, if X and Y are uncorrelated and the weight of X is two times the weight of Y, then the weight of the variance of X will be four times the weight of the variance of Y.
Suppose X is a coin flip with the probability of heads being h. Suppose that when X = heads then Y is drawn from a normal distribution with mean μ h and standard deviation σ h, and that when X = tails then Y is drawn from normal distribution with mean μ t and standard deviation σ t.
Diao H, Cheng N, Zhao Y, Xu H, Dong H, Thamm DH, Zhang D, Lin D. Ivermectin inhibits canine mammary tumor growth by regulating cell cycle progression and WNT signaling. BMC Vet Res. 2019 Aug 2;15 ...
Excessive fat around organs in midlife could contribute to Alzheimer’s risk due through neuroinflammation, the results of three small studies have suggested.
A plot, in blue, of for the curve y 2 = x 3 − 5x as X varies over the first 100000 primes. The X-axis is in log(log) scale -X is drawn at distance proportional to ( ()) from 0- and the Y-axis is in a logarithmic scale, so the conjecture predicts that the data should tend to a line of slope equal to the rank of the curve, which is 1 in ...