What is the probability of winning the lottery "6 out of 49"
with a single ticket
a) a “six”, b) a “five”, c) a “four”, d) a “three”,
e) to score at least one “three”?
f) How many bills do you have to tick to have at least one
“five”?
In: Statistics and Probability
When should we use other than classical interpretations of probability?
In: Statistics and Probability
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.2670.
Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
(a) What is the probability that among 18 randomly observed individuals exactly 5 do not cover their mouth when sneezing?
(b) What is the probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?
(c) Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? Why?
In: Statistics and Probability
1. Assume the economy can either be booming or in recession. The probability of a boom is 65%. If the economy is booming, a certain stock has an expected return of 20%. If the economy is in recession, the expected return of that same stock is 4%. What is the long term expected return of the stock?
2. Over the last year you observe that a certain company had a stock return of 24%, while the market had a return of 12%, and the risk-free rate was 2%. What would be your estimate of the firm's beta?
3. Assume a corporation is expecting the following cash flows in the future: $-4 million in year 1, $8 million in year 2, $21 million in year 3. After year 3, the cash flows are expected to grow at a rate of 4% forever. The discount rate is 12%, the firm has debt totaling $39 million, and 10 million shares outstanding. What should be the price per share for this company?
4. Stock A has a beta of 1.4, and stock B has a beta of 1.2. You invest 0.8% of your capital in stock A, and the rest in stock B. What is the beta of the resulting portfolio?
5. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 19 years, the coupon rate is 5% paid semiannually, and the discount rate is 17%.
What is the estimated value of this bond today?
6. As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 16 years, the coupon rate is 8% paid annually, and the discount rate is 13%.
What is this bond's coupon payment?
In: Finance
If a single card is drawn from an ordinary deck of a deck. Find
the
probability:
a. To the ace of diamonds
b. A 10
c. A queen or a heart
d. A 3 or a black card
In: Statistics and Probability
Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined by the following table:
| grade | A | B | C | D | F |
| probability | .25 | .35 | .2 | .15 | .05 |
(a) Using the usual numerical values for the grades, define the corresponding random variable, X, and its probability mass function, p(x).
(b) Calculate P(X ≤ 2), P(X < 2), and P(X ≥ 3).
(c) Plot the cumulative distribution function F(x).
(d) Compute the mean µ = E(X).
In: Statistics and Probability
Explain how and why the magnitude of a t value affects the probability of rejecting the null hypothesis, for negative and positive numbers.
In: Statistics and Probability
Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean mu and standard deviation sigma. ?Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigma and the maximum usual value mu plus 2 sigma. n
n=1510?, p=4/ 5
In: Statistics and Probability
The price of a bond is uniformly distributed between $60 and $100.
DO NOT SHOW WORK IN THE SPACE BELOW. You must attach a document to question 6 showing your work for problems 3-5 in order to receive credit. All files must be pdf format. You will receive a 0 grade for a question if you do not show work or give an explanation for your answer (graphs preferred).
In: Statistics and Probability
The price of a bond is uniformly distributed between $60 and $100.
DO NOT SHOW WORK IN THE SPACE BELOW. You must attach a document to question 6 showing your work for problems 3-5 in order to receive credit. All files must be pdf format. You will receive a 0 grade for a question if you do not show work or give an explanation for your answer (graphs preferred).
In: Statistics and Probability