QM1Notes 9

# D c the mean and standard deviation of a uniformly

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Unformatted text preview: calculated by b-a . d-c The mean and standard deviation of a uniformly distributed random variable is given by c+d d-c µ= ß= . 2 12 P(a < X < b) = 46 Example 1 Spinning a Dial Suppose that you spin the dial shown below so that it comes to rest at a random position. Model this with a suitable distribution, and use it to find the probability that the dial will land somewhere between 5˚ and 300˚. 0 270 90 180 The Normal Distribution A normal density function is a function of the form - f(x) = 1 e ß 2π (x-µ)2 2ß2 . µ = Mean ß = standard deviation The standard normal distribution has µ = 0 and ß = 1. We use Z rather than X to refer to the associated random variable. Tables The following tables give the probabilities P(Z ≤ z). Note Excel formula for this is =NORMSDIST(z) 47...
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