1. The sample space is the collection of all possible outcomes of a random experiment. De- scribe the sample space in each of the following situations: a) The price of a certain stock tomorrow. b) The number of companies that will default on their debt in March 2023. c) Stock of company A is currently selling for $100 a share. The time until the stock reaches $300. d) Price of the stock of two companies: A and B.
ANSWER:
a) The sample space for the price of a particular stock tomorrow specifies all possible values that the stock price can take. This sample space is usually represented by a set of real numbers, since stock prices can take any value within a certain range, including fractional values. For example, a particular company's share price may be $50, $75.34, or any other value in a possible range.
b) The sample space for the number of firms defaulting on their debt in March 2023 refers to the set of all possible values that the number of defaulting firms can take. This sample space is usually represented by the set of non-negative integers, since the number of defaulting firms can only be whole numbers (ie, 0, 1, 2, 3, etc.). For example, if 5 firms are expected to default in March 2023, the sample space set would be {0, 1, 2, 3, 4, 5}.
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