#reading-10-common-probability-distributions
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.
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Subject 1. Basic Definitionsw 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.
<span>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.
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