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

1.

Properties of probability function:

i) Properties of pmf: Probability mass function (X is a discrete random variable):

a. The probability that X can take a specific value is P(x). P[X=x]=P(x)

b. P(x) is non-negative for all real X.

c. The sum of P(x) over all possible values of X is 1.

​​​​ =1

ii) Properties of pdf: Probability density function (X is a continuous random variable):

a. The probability that X is between two points a and b is P[aXb] =

b. It is non-negative for all real X.

c. The integral of the probability function is 1, i.e., =1

2.

i) Theoretical Probability:

Theoretically, all "n" possible outcomes of a particular experiment are equally likely and a probability value is assigned to each possible outcome.

Example: The theoretical probability of rolling number 2 on a fair 6 sided die is 1/6 because 2 is one of the 6 possible outcomes.

ii). Experimental Probability:

We conduct an experiment large number of times and find the probability by using: number of favorable outcomes in the experiment/total number of trials.

Example: When a die is rolled 100 times. The number 4 appeared 20 times. The experimental probability of rolling number 4 =20/100. This may change for another experiment.

iii) SubjectiveProbability:

It is a probability value between 0 and 1 (0% - 100%) assigned by an individual based on how likely he/she thinks that an event will occur.

Example: The probability of getting rainfall today is 0.5 (i.e.,50%).