1. Properties of the uniform, normal, and exponential distributions Aa Aa Suppos

Question

1. Properties of the uniform, normal, and exponential distributions Aa Aa Suppose that x1 is a uniformly distributed random variable, x2 is a normally distributed random variable, and X3 is arn exponentially distributed random variable. For each of the following statements, indicate whether it applies to x1, X2, and/or x3. Check all that apply. X1 x2 X3 (uniform) (normal) (exponential) The graph of the probability density function is perfectly symmetrical about the mean. The probability that x equals its expected value is 0. x cannot assume a negative value.

Explanation / Answer

Note: There are two types of uniform distribution - discrete and continuous. Discrete uniform distribution can have non-zero probability that x equals its expected value (or more strictly 1). Probability that x equals its expected value is generally zero for continuous distributions.

x1 (uniform) x2 (normal) x3 (exponential) The graph of the probability density function is perfectly symmetrical about the mean. The probability that x equals its expected value is 0. x cannot assume a negative value.

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