Question

Probability Concept

FIN 3309

1. Properties of Probability function

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2. 3 different types of probabilities

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3. You have a bag of m&ms with only 12 left. There is 3 red, 4 yellow, 5 blue. What is the probability that you will get a red m&m? What is the odds that you would choose red?

4. You are given the following probability distribution for the annual sales of ElStop Corporation:

Probability Distribution for ElStop Annual Sales

Probability Sales ($ Millions)

0.20 275

0.40 250

0.25 200

0.10 190

0.05 180

sum = 1.00

• Calculate the expected value of ElStop’s annual sales.

• Calculate the variance of ElStop’s annual sales.

• Calculate the standard deviation of ElStop’s annual sales.

5. An analyst developed two scenarios with respect to the recovery of $100,000 principal from defaulted loans is:

Scenario Probability of Scenario (%) Amount Recovered ($) Probability of Amount (%)

1 40 50,000 60

30,000 40

2 60 80,000 90

60,000 10

What is the amount of the expected recovery?

6. Calculate the covariance of the returns on Bedolf Corporation (RB) with the returns on Zedock Corporation (Rz), using the following data.

Probability Function of Bedolf and Zedock Returns

RZ = 15% RZ = 10% RZ = 5%

RB = 30% 0.25 0 0

RB = 15% 0 0.50 0

RB = 10% 0 0 0.25

Answer 1

Note - The first 4 questions are solved completely.

Properties of Probability Distribution

1. The probability that x can take a specific value is p(x)
2. p(x) is non negative for all real x
3. The sum of p(x) over all possible values of x is 1.

(Note - These are taken from the textbook, please refer to your textbook for more specific words)

3 types of theoretical probability
- Theoretical probability
-Theoretical probability
-Personal or subjective probability

3. You have a bag of m&ms with only 12 left. There is 3 red, 4 yellow, 5 blue. What is the probability that you will get a red m&m? What is the odds that you would choose red?

A probability of getting red m&m = 3/12
Complement of the this probability = 1- 3/12 = 12

Odds Ratio =

4. Probability Distribution
Calculate the expected value of ElStop’s annual sales.

Let f(x) be the probability
x be the sales

Calculate the variance of ElStop’s annual sales.

Calculate the standard deviation of ElStop’s annual sales