Common Probability Distributions

Question 1

Define probability distribution

Answer 1

The probabilities of possible outcomes of a random variable

Question 2

Distinguish between discrete and continuous random variables and their probability functions

Answer 2

Stock Prices: Discrete Random Variable: Finite number of outcomes (heads or tail, A-F for grades, black or white)

Stock Returns: Continuous Random Variable: Cannot count or list all possible outcomes (predicting the weather)

Question 3

Describe the set (range) of possible outcomes of a specified discrete random variable

Answer 3

Lowest to Highest: Bonds: Lowest value of 0, maximum value of par value + sum of coupon payments (which assumes Int rate is 0, which indicates that the sum of the price of the bond is the face value)

Ex: 1000 FV, 5%, 10 yr coupon bond
Find all possible values (all possible values are lowest to highest) or $0 to %1,500 aka Future Value

Question 4

Interpret a cumulative distribution function

Answer 4

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Question 5

Calc, interpret probabilities for a random variable, given its cumulative distribution function

Answer 5

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Question 6

9e. Define a discrete uniform random variable, and which random variables would be most likely to follow a discrete uniform distribution?

Answer 6

To follow a discreet uniform distribution.

Discreet eandom variables are ‘discreet’ or equally likely in outcome.

A discreet random distribution is one where there are ‘n’ discrete, equally likely outcomes. a discreet uniform distribution has ‘n’ possible outcomes, the prob. For each outcome =’s 1/n

The discreet uniform dist. Is characterized by an equal probability for each outcome. A single die roll is an often-used example of a uniform distribution. In combining two random variables, such as a coin flip or die roll outcomes, the sum will not be uniform army distributed.

Question 7

Define a Bernoulli random variable

Answer 7

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Question 8

Define a Binomial random variable

Answer 8

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Question 9

Calc, interpret probabilities given the discrete uniform and the binomial distribution functions

Answer 9

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Question 10

construct a binomial tree to describe stock price movements

Answer 10

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Question 11

Calc, interpret tracking error

Answer 11

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Question 12

Define the continuous uniform distribution

Answer 12

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Question 13

Calc, interpret probabilities given a continuous uniform distribution

Answer 13

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Question 14

Explain the key properties of the normal distribution

Answer 14

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Question 15

Distinguish between a univariate and a multivariate distribution

Answer 15

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Question 16

Explain the role of correlation in the multivariate normal distribution.

Answer 16

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Question 17

Determine the probability that a normally distributed random variable lies inside a given interval

Answer 17

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Question 18

Define the standard normal distribution

Answer 18

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Question 19

Explain how to standardize a random variable

Answer 19

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Question 20

Calc, interpret probabilities using the standard normal distribution

Answer 20

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Question 21

Define shortfall risk

Answer 21

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Question 22

Calc the safety-first ratio

Answer 22

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Question 23

Select an optimal portfolio using Roy’s safety-first criterion

Answer 23

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Question 24

Explain the relationship between normal and lognormal distributions

Answer 24

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Question 25

Explain why the lognormal distribution is used to model asset prices

Answer 25

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Question 26

Distinguish between discretely and continuously compounded rates of return

Answer 26

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Question 27

Calc, interpret a continuously compounded rate of return, given a specific holding period return.

Answer 27

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Question 28

Explain Monte Carlo Simulation and describe its major applications and limitations

Answer 28

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Question 29

Compare Monte Carlo simulation and Historical Simulation

Answer 29

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