Common Probability Distributions Flashcards
Define probability distribution
The probabilities of possible outcomes of a random variable
Distinguish between discrete and continuous random variables and their probability functions
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)
Describe the set (range) of possible outcomes of a specified discrete random variable
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
Interpret a cumulative distribution function
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Calc, interpret probabilities for a random variable, given its cumulative distribution function
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9e. Define a discrete uniform random variable, and which random variables would be most likely to follow a discrete uniform distribution?
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.
Define a Bernoulli random variable
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Define a Binomial random variable
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Calc, interpret probabilities given the discrete uniform and the binomial distribution functions
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construct a binomial tree to describe stock price movements
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Calc, interpret tracking error
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Define the continuous uniform distribution
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Calc, interpret probabilities given a continuous uniform distribution
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Explain the key properties of the normal distribution
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Distinguish between a univariate and a multivariate distribution
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Explain the role of correlation in the multivariate normal distribution.
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Determine the probability that a normally distributed random variable lies inside a given interval
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Define the standard normal distribution
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Explain how to standardize a random variable
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Calc, interpret probabilities using the standard normal distribution
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Define shortfall risk
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Calc the safety-first ratio
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Select an optimal portfolio using Roy’s safety-first criterion
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Explain the relationship between normal and lognormal distributions
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Explain why the lognormal distribution is used to model asset prices
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Distinguish between discretely and continuously compounded rates of return
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Calc, interpret a continuously compounded rate of return, given a specific holding period return.
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Explain Monte Carlo Simulation and describe its major applications and limitations
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Compare Monte Carlo simulation and Historical Simulation
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