Question

In: Statistics and Probability

The investing activities of THE WALL STREET JOURNAL INTERACTIVE EDITION subscribers show that the average annual...

The investing activities of THE WALL STREET JOURNAL INTERACTIVE EDITION subscribers show that the average annual number of stock transactions is approximately 15. Suppose a certain investor transacts this frequently. In addition, suppose that the probability of a transaction, for this investor, is the same for any two months, and that the transactions in one month are independent of those that it makes in any other month.
a. What is the average number of transactions per month?
b. What is the probability that there will be no stock transactions for a month?
c. What is the probability that there will be exactly one transaction for a month
d. What is the probability that there will be more than one transaction per month

Solutions

Expert Solution

We can model the number of stock transactions in a given time period by Poisson distribution as it satisfies below conditions.

  • The experiment results in outcomes that can be classified as successes (transaction) or failures (no transaction).
  • The average number of successes (transactions) that occurs in a specified region (duration) is known.
  • The probability that a success (transaction) will occur is proportional to the size of the region (duration).
  • The probability that a success (transaction) will occur in an extremely small region (duration) is virtually zero.

a.

Average number of transactions per month = 15/12 = 1.25

b.

X ~ Poisson( = 1.25)

probability that there will be no stock transactions for a month = P(X = 0)

= 0.2865

b.

probability that there will be exactly one transaction for a month = P(X = 1)

= 0.3581

c.

probability that there will be more than one transaction per month = P(X > 1)

= 1 - P(X = 0) - P(X = 1)

= 1 - 0.2865 - 0.3581

= 0.3554

orchestra answered 2 years ago
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