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Example:Random variable X follows a continuous uniform distribution over 12 to 28, that is a = 12, and b = 28. The probability of an outcome between 15 and 25 is:
P(15 ≤ X ≤ 25) = (25 - 15) / (28 - 12)
= 10 / 16 = 0.625
l: Explain the key properties of the normal distribution.
The normal distributionhas the following key properties:
It is completely described by its mean and variance, we write X ~ N(μ, σ2). In words, this says that "X" is normally distributed with mean μ and variance σ2.
Skewness = 0. This means the normal distribution is symmetric about its mean, so that P(X ≤ μ) = P(μ ≤ X) = 0.5, and mean = median = mode.
Kurtosis = 3; this is a measure of how "flat" the distribution is. Recall that excess kurtosis is measured relative to the number "3."
A linear combination of normally distributed random variables is also normally distributed.
