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Probability Distributions Flashcards

1
Q

Probability distribution

A

A probability distribution lists all the possible outcomes of an experiment, along with their associated probabilities.

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2
Q

Discrete Random Variable

A

A Discrete Random Variable has positive probabilities associated with a finite number of outcomes.

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3
Q

Continuous Random Variable

A

A continuous random variable has positive probabilities associated with a range of outcome values–the probability of any single value is zero.

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4
Q

Set of possible outcomes of a specific discrete random variable

A

Finite set of values (in a discrete distribution, p(x)=0 if it cannot happened, and p(x)>0 if it can).

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5
Q

Probability Function

A

P(X=x) = p(x), such that 0<=1 and Σp(x)=1

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6
Q

Probability Density Function (pdf)

A

Function for a continuous random variable used to determine the probability it will fall in a particular range

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7
Q

Cumulative Distribution Function (cdf)

A
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8
Q

Discrete Uniform Distribution

A

Distribution where there are n discrete, equally likely outcomes.

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9
Q

Binomial Distribution

A

Probability distribution for a binomial (discrete) random variable that has two possible outcomes.

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10
Q

Probability of an outcome under a discrete uniform distribution

A

1/n

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11
Q

Probability of an outcome under binomial distribution (with p = probability of success)

A
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12
Q

Binomial tree

A

Illustrates the probabilities of all the possible values that a varaible can take on given the probability of an up-move and the magnitude of an up-move

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13
Q

Continuous Uniform Distribution

A

The probability of X occuring in a possible range is the length of the range relative to the total of all possible values. If a and b are the limits, then:

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14
Q

Normal Probability distribution

A

1) it is symmetrical and bell-shaped with a peak in the center
2) mean = median = mode,
3) the normal distribution is defined by the

mean and standard deviation; skew = 0; kurtosis = 3

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15
Q

Multivariate Distribution

A

Describes the probabilities for more than one random variable

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16
Q

Univariate Distribution

A

Describes the probabilities for a single random variable

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17
Q

Confidence interval

A

The range within which we have a given level of confidence of finding a point estimate

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18
Q

90% confidence interval

A

μ +/- 1.65 standard deviations

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19
Q

95% confidence interval

A

μ +/- 1.96 standard deviations

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20
Q

99% confidence interval

A

μ +/- 2.58 standard deviations

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21
Q

Probability that a normally distributed random variable X will be within A standard deviations of its mean

A

Twice the cumulative left-hand tail probability F(-A), where F(A) is the cumulative standard normal probability of A

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22
Q

z-table

A

Used to find the probability that X will be less than or equal to a given value

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23
Q

P(X<>

A
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24
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P(X>x)

A
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25
Q

Shortfall risk

A

The probability that a portfolio’s value (or return) will fall below a specific value over a given time.

Greater safety-first ratios indicate a smaller shortfall risk.

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26
Q

Roy’s safety-first criterion

A

The optimal portfolio minimizes shortfall risk.

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27
Q

Lognormal distribution

A

If x is normally distributed, e^x follows a lognormal distribution.

A lognormal distribution is often used to model asset prices, since it cannot be negative and can take on any positive value.

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28
Q

The continuously compounded rate via HPR

A

ln ( 1 + HPR )

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29
Q

Monte Carlo simulation

A

Use of randomly generated values for risk factors, based on their assumed distributions, to produce a distribution of possible security values.

It is complex and will provide answers no better than assumptions used.

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30
Q

Historical simulation

A

Randomly selected past values to generate a distribution of possible security values. It cannot consider the effects of significant events that did not occur in a sample period.

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31
Q

Standardization of a random variable

z =

A
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32
Q

Sharpe Ratio

A
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33
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Treynor Ratio

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34
Q

Probability Function

A

It specifies the probability that a random variable is equal to a specific value

In other words it is the probability that random variable X takes on value x or p(x) = P(X = x )

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35
Q

Shortfall Risk

A

Shortfall Risk is the probability that a portfolio value or return will fall below a particular target value or return over given time period

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36
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37
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38
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39
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40
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48
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Variance in terms of Expected Value

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50
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Safety-first ratio for portfolio P

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54
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S

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55
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Properties of Cummulative Distribution Function

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56
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Properties of Univariate or Multivariate Distributions

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74
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Standard Deviation other Formula

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75
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Standard Deviation other Formula

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76
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How to find negative Z values

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