STA220H5 Chapter Notes - Chapter 4.1: Random Variable, Standard Deviation
4.1-4.3
Random variables that can assume a countable number of values are called discrete.
Random variables that can assume values corresponding to any of the points
contained in an interval are called continuous.
The probability distribution of a discrete random variable is a graph, table, or
formula that specifies the probability associated with each possible value that the
random variable can assume.
Requirements for the probability distribution of a discrete random variable x
1. P(x) 0 for all values of x
2. P(x)=1
3. Where the summation of p(x) is over all possible values of x.*
The mean, or expected value, of a discrete random variable x is
U=E(x)=xp(x)
The variance of a random variable x is
The standard deviation of a discrete random variable is equal to the square root of
the variance, or
Probability rules for a discrete random variable
Let x be a discrete random variable with probability distribution p(x), mean u, and
standard deviation. Then, depending on the shape of p(x) , the following probability
statements can be made:
Chebyshev’s rule
Empirical rule
Applies to any probability distribution
(see figure 4.6a)
Applies to probability distributions that
are mound shaped and symmetric (see
figure 4.6b)
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Document Summary
Random variables that can assume a countable number of values are called discrete. Random variables that can assume values corresponding to any of the points contained in an interval are called continuous. The probability distribution of a discrete random variable is a graph, table, or formula that specifies the probability associated with each possible value that the random variable can assume. Requirements for the probability distribution of a discrete random variable x: p(x) 0 for all values of x, p(x)=1, where the summation of p(x) is over all possible values of x. The mean, or expected value, of a discrete random variable x is. The variance of a random variable x is. The standard deviation of a discrete random variable is equal to the square root of the variance, or. Let x be a discrete random variable with probability distribution p(x), mean u, and standard deviation.
