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STATLECT > Probability distributions > Uniform distribution

Uniform distribution - Exercise set 1

This exercise set contains some solved exercises on the uniform distribution. The theory needed to solve these exercises is introduced in the lecture entitled Uniform distribution.

Exercise 1.1

Let X be a uniform random variable with support[eq1] Compute the following probability:[eq2]

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We can compute this probability either using the probability density function or the distribution function of X. Using the probability density function:[eq3]Using the distribution function:[eq4]

Exercise 1.2

Suppose the random variable X has a uniform distribution on the interval [eq5]. Compute the following probability:[eq6]

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This probability can be easily computed using the distribution function of $X $:[eq7]

Exercise 1.3

Suppose the random variable X has a uniform distribution on the interval $left[ 0,1 ight] $. Compute the third moment of X, i.e.:[eq8]

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We can compute the third moment of X using the transformation theorem:[eq9]

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