Calculate the expected value, the variance, and the standard...

Calculate the expected value, the variance, and the standard deviation of the given random variable $X$. (You calculated the expected values in the Section 8.3 exercises. Round all answers to two decimal places.)
$X$ is the number of tails that come up when a coin is tossed twice.

Key Concepts

Random Variable

A random variable is a function that assigns a numerical value to each outcome in a sample space of a random experiment. It provides a quantitative description of the outcomes, allowing the application of mathematical techniques to study randomness and uncertainty.

Discrete Probability Distribution

A discrete probability distribution describes the probabilities of occurrence of different outcomes for a discrete random variable. Each possible value of the random variable is associated with a specific probability, and the sum of these probabilities equals one.

Expected Value

The expected value of a random variable is the long-run average or mean of its values when the experiment is repeated many times. It is computed as the sum of each possible value multiplied by its corresponding probability, and it represents the center of the distribution.

Variance

Variance is a measure of the spread or dispersion of a random variable's values around the expected value. It is calculated by taking the weighted average of the squared differences between the values and the mean, providing insight into the variability of the outcomes.

Standard Deviation

The standard deviation is the square root of the variance and reflects the average distance of the data points from the mean. It is expressed in the same units as the random variable and offers a clear measure of the spread of the probability distribution.

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