Quant - Probability Trees Flashcards

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1
Q

How is the expected value of a random variable calculated?

A

The expected value of a random variable is a probability-weighted average of the possible outcomes of the random variable.

For a random variable X, the expected value of X is denoted E(X).

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2
Q

What is the “variance” of a random variable?

A

The variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value E(X): σ2(X) = E{[X − E(X)]2}, where σ2(X) stands for the variance of X.

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3
Q

What are the units of “standard deviation”?

A

The same as of the dataset.

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4
Q

What does a probability tree illustrate?

A

A probability tree is a means of illustrating the results of two or more independent events.

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5
Q

What is a “conditional probability”?

A

the probability of an event given (conditioned on) another event is a conditional probability.

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6
Q

How do you calculate the “conditional expected value”?

A

Conditional expected value is E(X | S) = P(X1 | S)X1 + P(X2 | S)X2 + … + P(Xn | S)Xn and has an associated conditional variance and conditional standard deviation.

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7
Q

With respect to investing, what is the typical application of Bayes’ forumla?

A

Bayes’ formula is a method used to update probabilities based on new information.

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8
Q

What is the “investment version” of Bayes’ formula?

A

Updated probability of event given the new information =
[
(Probability of the new information given event)
/
(Unconditional probability of the new information)
] × Prior probability of event.

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9
Q

What does it mean if the variance of an event is zero?

A

If variance is 0, there is no dispersion or risk. The outcome is certain, and the quantity X is not random at all.

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10
Q

How do you calculate the variance of a random variable?

A

the probability-weighted average of squared deviations from the random variable’s expected value

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11
Q

How do you calculate the standard deviation of a random variable?

A

take the square root of the variance.

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12
Q

What is “conditional variance”?

A

The variance of one variable, given the outcome of another.

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13
Q

What are “prior probabilities”?

A

Probabilities reflecting beliefs prior to the arrival of new information.

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14
Q

What are “posterior probabilities”?

A

An updated probability that reflects or comes after new information.

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