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If you toss a coin 3 times, the possible outcomes are as follows (where H means heads and T means tails): TTT, TTH, THT, HTT, THH, HTH, HHT, HHH.

In total, there are 8 possible outcomes. Of these:

- Only 1 (TTT) has 0 heads occurring.
- Three (TTH, THT and HTT) have 1 heads occurring.
- Three (THH, HTH and HHT) have 2 heads occurring.
- One (HHH) has 3 heads occurring.

Thus, if x = number of heads in 3 tosses of a coin, then x = 0, 1, 2 or 3.

Now, the respective probabilities are 1/8, 3/8, 3/8 and 1/8, as you have just seen. So:

p(0) = p(0 Heads) = 1/8

p(1) = p(1 Head) = 3/8

p(2) = p(2 Heads) = 3/8

p(3) = p(3 Heads) = 1/8

This is a probability distribution; it records probabilities for each possible outcome of the random variable.

A table, graph or rule that associates a probability P(X=x

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Statistics computed from discrete variables are continuous. The mean on a five-point scale could be 3.117 even though 3.117 is not possible for an individual score.

For any random variable, it is necessary to know two things:

- the list of all possible values that the random variable can take on.
- the probability of each value occurring.

These give a probability distribution. The first item on the list is called the range.

With regard to the range of possible outcomes of a specified random variable:

**Sometimes the possible values of a random variable have both lower and upper bounds.**For example, there are three possible values of the number of heads showing face-up on two tosses of a coin: 0, 1, and 2. Therefore, the lower bound is 0 and the upper bound is 2.**Sometimes the lower bound exists, but the upper bound does not.**For example, the lower bound of the price of a stock is 0, since it cannot fall below 0. However, there is no upper bound on the price (at least theoretically).**Sometimes the upper bound exists, but the lower bound does not.**Consider the profit or loss of the seller of a call option. Suppose the buyer pays the seller $2 to buy a call option, which gives the buyer the right to buy a stock at $10 by the end of 2006. The maximum profit the seller can make is $2, but the maximum loss the seller may incur is unlimited since there is no upper bound on the possible values of stock prices.**In other cases, neither bound is obvious.**Consider the profit or loss of a big company. In a good year, profits could be as high as dozens of billions of dollars, losses could be equivalent in a very bad year.

rethan: Discrete=limited |

Daddykay: Not necessarily |

arsand: Its rather what values the random value can take limit had no relation.. to the nature |