2.9.A—Calculate the mean and standard deviation for a discrete random variable

Calculate the mean and standard deviation for a discrete random variable.

• A numerical value measuring a characteristic of a probability distribution of a random variable, or a population, is a parameter. The value of a parameter is a single, fixed value.
• The expected value (or mean) of a probability distribution is a parameter and is denoted by EX( ) or µX. For a discrete random variable X, the expected value is calculated as μXi =∑xP. ()x ,i where xi is the possible value of the random variable and P()xi is the probability of the possible value of the random variable. The expected value can be interpreted as the long-run average outcome of the random variable. The discrete random variable can only take on values that are countable or finite.
• The standard deviation of a probability distribution is a parameter represented by SD X() or σX. For a discrete random variable X, the standard deviation is calculated as σ μXi i X xP x=∑ -() . () 2 , where xi is the possible value of the random variable, µX is the mean, and P()xi is the probability of the possible value of the random variable. The standard deviation can be interpreted as the typical deviation of the values of the random variable from the mean value (or expected value) of the random variable over the long run. The square of the standard deviation of a random variable is called the variance of the random variable and is denoted as VX() or σ2 X. Probability, Random Variables, and Probability Distributions UNIT 2