Quantitative Problem: You are given the following probability distribution for CHC Enterprises:

What is the stock's expected return? Round your answer to 2 decimal places. Do not round intermediate calculations.
%

What is the stock's standard deviation? Round your answer to two decimal places. Do not round intermediate calculations.
%

What is the stock's coefficient of variation? Round your answer to two decimal places. Do not round intermediate calculations.

Table 1: Survival probability Year Probability of surviving from start of year to end of year

Year 1 - 0.75

Year 2 . - 0.58

Year 3 - 0.37

Year 4 - 0.23

Year 5 - 0 e.

Jackson will use $50,000 from the total sale proceed of instruments as a single premium to purchase an annuity today. This annuity pays X at the end of each year while Jackson is alive. The estimated probability of Jackson surviving for the next 5 years is stated in table 1. The yield rate is assumed to be j1 = 3.2% p.a. Calculate X value. Round your answers to three decimal places. Draw a detailed contingent cash flow diagram for instrument D, from the perspective of Jackson

Stocks A and B have the following probability distributions of expected future returns: PROBABILITY: 0.1, 0.2, 0.4, 0.2, 0.1 Stock A: 8%, 5,13, 21,29 Stock B. 36%, 0, 22, 25, 36. Calculate the expected rate of return, rB, for Stock B (rA = 12.50%.) Do not round intermediate calculations. Round your answer to two decimal places. Calculate the standard deviation of expected returns, ?A, for Stock A (?B = 19.68%.) Do not round intermediate calculations. Round your answer to two decimal places. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

Compare and contrast 'probability' and 'possibility.' Include how you would define the two terms - probability and possibility - in a way that clearly defines each, distinguishes them, and describes the differences that are important in the field of statistics. Consider finding an example of the application of the concepts of probability in your own life that illustrates, at least in part, what you described about probability and possibility, and tell us about it. Are meaningful inferential statistics dependent on both probability and possibility? Why or why not? Any other insights or thoughts about the concepts of probability?

Discrete Mathematics Probability Worksheet Name __________________________________________

(1) Two ordinary dice are rolled. Find the probability that ...

(a) ... the sum of the dice is 6, 7 or 8.

(b) ... the sum of the dice is 5 or at least one of the dice shows a 5

.(c) ... the two dice match.

(2) A card is drawn from an ordinary deck of 52 cards. Find the probability that the card is ...

(a) ... an ace or a heart

.(b) ... an ace or a black card

.(c) ... a diamond, a club, or a king.

(3) Two cards are drawn from deck, with replacement. (This means that one person chooses a card,looks at it and returns it, and then another person chooses a card, looks at it, and returns it.) What is the probability that ...

(a) ... the first card is an ace and the second card is black?

(b) ... both cards are spades?

(c) ... neither card has a value from {2, 3, 4, 5}?(d) ... at least one card is an ace?

(e) ... the first card is an ace or the second card is black?

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles are pulled out at once (i.e. with no particular order). What is the probability that ...

(a) ... all four marbles are red?

(b) ... more of the marbles are green than red?

(c) ... both red and green marbles are present?

(d) ... two of the marbles chosen are both labeled "5"?

(5) What is the probability that a five card hand dealt from a standard deck of cards will include fourcards of the same value? (This kind of hand is called a "four of a kind" in Poker.)

(6) A fair coin is tossed ten times in a row.

(a) What is the probability that "heads" comes up exactly five times?

(b) What is the probability that "heads" come up at least eight times?

(c) What is the probability that "heads" come up at least once?

You flip a coin 8 times. What is the probability of seeing exactly four tails?

128/256

186/256

70/256

4/256

(7) Let's say the probability of having a particular cancer is 1%.There is a test for this cancer. It will test positive 90% of the time if you have the cancer and it will correctly come out negative 80% of the time if you don't have the cancer.

Fill out the following probabilities:

Pr(cancer) = 0.01

Pr(no cancer) =

Pr(positive | cancer) = 0.9

Pr(negative | cancer) =

Pr(positive | no cancer) =

Pr(negative | no cancer) = 0.8

(8) By the product rule, the probability of the test coming out positive and you have cancer is:

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

A.Calculate the expected rate of return, r_B, for Stock B (r_A = 10.10%.) Do not round intermediate calculations. Round your answer to two decimal places.
%

B.Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 22.00%.) Do not round intermediate calculations. Round your answer to two decimal places.
%

C. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

Is it possible that most investors might regard Stock B as being less risky than Stock A?

1. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
2. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
3. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
4. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
5. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.

1. A randomly selected freshman takes English with probability 0.7, takes Math with probability 0.5, and takes either English or Math with probability 0.8. What is the probability of taking both English and Math?

2. Two mutually exclusive events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

3. Two independent events A and B have P(A) = 0.2, P(B) = 0.3. Find P (A or B).

4. If P (A | B) = 0.8 and P(B) = 0.6, find P (A and B).

5. Given the following table, evaluate

P(No), P (Woman and Yes), P (Man | Yes), P (No opinion | Woman), P(Men or No Opinion).

Are Women and No mutually exclusive?

Are Women and No independent?

6. A box contains 5 blue chips, 4 red chips, and 7 green chips. Select 10 chips at random.

1. In how many ways can this be done?
2. How many of these selections consist of 3 blue chips, 2 red chips, and 5 green chips?

(do not simplify your answers, leave them in terms of binomial coefficients).

Explain in plain language how a standard probability weighting function (i.e. underestimating the probability of very likely events and overestimating the probability of very unlikely events) can lead a person to simultaneously gamble and purchase insurance

Question 1: Given the following probability distributions for stock A and stock B

Calculate (a) expected return, (b) standard deviation (c) coefficient of variation for each stock (analyze single stock separately: do expected return for A, standard deviation for A, CV for A. Then repeat the steps for stock B)