By Voloshynovskiy, Herrigel, Baumgaertner, Pun

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The face is shaped differently from the tail. But such physical complications are beside the point! We know what we mean by fair and most coins, if they have not been damaged in some way, will be at least approximately fair. In the previous paragraph, we've described two practically related but logically distinct ideas of probability: probability as "long-run relative frequency" and probability as determined by symmetry. There are other notions of probability. There is probability as "degree of rational belief," the degree of belief a rational person would invest in a given statement.

So, for example, with one dot, you lose five dollars and with six dots you gain ten dollars. Would you play this game? 3 - Linear Functions of a Random Variable 21 In a great variety of transactions like this one, your net result Y comes through a linear equation from a physically determined random variable X. A linear equation is an equation in which all variables appear added together with coefficients, but without any powers, square roots, and so on. For a linear equation, the standard notation is a, b constants, Y=a+bX in the example Y = -8+3X a = -8, b = 3.

Let X = 1 if the tack falls with the point up and let X = 0 otherwise. Write your gain/loss random variable as a function of X. Then compute the mean and variance of X and use that information to compute the mean and standard deviation of your gain/loss in this game. 7(d). Show how. (e) Would you play this game? (f) Suppose you receive five dollars when the tack falls with the point up and lose five dollars otherwise. Which game would you prefer, this one or the one in part (c)? 3 The Scottish physicist james D.

### A Stochastic Approach to Content Adaptive Digital Image Watermarking by Voloshynovskiy, Herrigel, Baumgaertner, Pun

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