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Probability and Statistics II week 9

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3.1. UNIFORM DISTRIBUTIONS: SPECIAL PROBABILITY DENSITY FUNCTIONS In this section we shall study some of the probability densities that figure most prominently is statistical theory and in applications. 3.2.1. THE UNIFORM DISTRIBUTION Definition 3.2.1. A random variable X has a uniform distribution and it is referred to as a continuous uniform random variable if and only if its probability density function is given by The shape of a uniform distribution is shown in Fig. 1 below:   The Mean, Variance and Moment generating function of the Uniform Distribution Now we want to evaluate E (x2). We want to evaluate the m.g.f.

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