By Fearn T., Brown P.J., Besbeas P.

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**Additional info for A Bayesian decision theory approach to variable selection for discrimination**

**Sample text**

38. Urn 1 contains two white balls and one black ball, while urn 2 contains one white ball and five black balls. One ball is drawn at random from urn 1 and placed in urn 2. A ball is then drawn from urn 2. It happens to be white. What is the probability that the transferred ball was white? 39. Stores A, B, and C have 50, 75, and 100 employees, and, respectively, 50, 60, and 70 percent of these are women. Resignations are equally likely among all employees, regardless of sex. One employee resigns and this is a woman.

Let X be such a random variable. 6) f (x) dx B The function f (x) is called the probability density function of the random variable X. 6) states that the probability that X will be in B may be obtained by integrating the probability density function over the set B. Since X must assume some value, f (x) must satisfy ∞ 1 = P {X ∈ (−∞, ∞)} = −∞ f (x) dx All probability statements about X can be answered in terms of f (x). 7) a If we let a = b in the preceding, then a P {X = a} = f (x) dx = 0 a In words, this equation states that the probability that a continuous random variable will assume any particular value is zero.

1. 4 Suppose that our experiment consists of seeing how long a battery can operate before wearing down. Suppose also that we are not primarily interested in the actual lifetime of the battery but are concerned only about whether or not the battery lasts at least two years. In this case, we may define the random variable I by I= 1, 0, if the lifetime of battery is two or more years otherwise If E denotes the event that the battery lasts two or more years, then the random variable I is known as the indicator random variable for event E.

### A Bayesian decision theory approach to variable selection for discrimination by Fearn T., Brown P.J., Besbeas P.

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