The document discusses variance as a measure of the amount of variation of a random variable from its expected value. It provides examples such as the variance of rolling a six-sided die, which is , and the variance of tossing a coin twice and counting the number of heads, which is 1. Variance takes into account all possible values and their probabilities rather than just the extremes.

1. Suppose that a deck of n cards numbered 1, 2, . . . . n is thoroughly shuffled and dealt. For 1
Solution
Examples The variance of a random variable or distribution is the expectation, or
mean, of the squared deviation of that variable from its expected value or mean. Thus the
variance is a measure of the amount of variation of the values of that variable, taking account of
all possible values and their probabilities or weightings (not just the extremes which give the
range). For example, a perfect six-sided die, when thrown, has expected value of Its expected
absolute deviation—the mean of the equally likely absolute deviations from the mean—is But
its expected squared deviation—its variance (the mean of the equally likely squared
deviations)—is As another example, if a coin is tossed twice, the number of heads is: 0 with
probability 0.25, 1 with probability 0.5 and 2 with probability 0.25. Thus the expected value of
the number of heads is: this example will be helpful for you