Probability distribution of a random variable

Reference no: EM1379270

An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based past data.

NARREND

1. {Mutual Fund Price Narrative} Which approach was used to produce this figure?

2. {Mutual Fund Price Narrative} Interpret the 75% probability.

3-4. The sample space of the toss of a balanced coin is S = {1, 2, 3, 4, 5, 6}. If the die is balanced, each simple event (outcome) has the same probability. Find the probability of the following events:

a.	Rolling an odd number
b.	Rolling a number less than or equal to 3

NARRBEGIN: Financial Consultants

Financial Consultants

A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

	Portfolio Composition
Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.10	0.15

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

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5. {Financial Consultants Narrative} Find the following probabilities:

a.	P(A)

6. {Financial Consultants Narrative} Express each of the following events in words:

A or B

7. {Financial Consultants Narrative} Find P(A and B).

8. {Financial Consultants Narrative} Express each of the following probabilities in words:

P(A|B)

Blackjack

The probability distribution of a random variable X is shown below, where X represents the amount of money (in $1,000s) gained or lost in a particular game of Blackjack.

x	-4	0	4	8
p(x)	0.15	0.25	0.20	0.40

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9. {Blackjack Narrative} Find the following probabilities:

P(X£ 0)

10. {Blackjack Narrative} Find the following values, and indicate their units.

E(X)

NARRBEGIN: Montana Highways

Montana Highways

A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit.

11. {Montana Highways Narrative} What is the distribution of X?

12. {Montana Highways Narrative} Find P(X = 10).

NARRBEGIN: Subway Waiting Time

Subway Waiting Time

At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.

13. {Subway Waiting Time Narrative} What is the probability density function for this uniform distribution?

14. {Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

NARRBEGIN: Battery Life

NARRBEGIN: IT Graduates Salary

IT Graduates Salary

The recent average starting salary for new college graduates in IT systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.

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15. {IT Graduates Salary Narrative} Is this a continuous probability distribution or discrete probability distribution?

16. {IT Graduates Salary Narrative} What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

17. {IT Graduates Salary Narrative} What is the probability of a new graduate getting a starting salary in excess of $55,000?

18. {IT Graduates Salary Narrative} What percent of starting salaries are no more than $42,250?

19. {IT Graduates Salary Narrative} What is the cutoff for the bottom 5% of the salaries?

20. {IT Graduates Salary Narrative} What is the cutoff for the top 3% of the salaries?

Reference no: EM1379270

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