Probability, hypothesis testing, regression, simulation and time series.
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- Define probability in quantitative finance
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The likelihood of an event occurring, expressed as a number between 0 and 1- State the Law of Large Numbers
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As the number of trials increases, the sample average converges to the expected value- What is conditional probability?
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The probability of event A given that event B has occurred, denoted P(A|B)- State Bayes' Theorem in formula form
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P(A|B) = P(B|A) * P(A) / P(B)- Distinguish independent and mutually exclusive events
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Independent events can occur simultaneously; mutually exclusive events cannot- Define a probability distribution
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A function that assigns probabilities to all possible values of a random variable- What is expected value?
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The weighted average of all possible outcomes, denoted E(X)- Define variance in probability
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The measure of spread or dispersion of a random variable around its expected value- What is the null hypothesis?
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The default assumption that no effect or difference exists; the claim tested against- Define Type I error
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Rejecting the null hypothesis when it is actually true (false positive)- Define Type II error
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Failing to reject the null hypothesis when it is actually false (false negative)- What is the p-value?
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The probability of observing a test statistic as extreme as the one observed, assuming the null hypothesis is true- Define the significance level
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The probability threshold for rejecting the null hypothesis, typically 0.05 or 5%- What is statistical power?
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The probability of correctly rejecting the null hypothesis when it is false (1 minus Type II error rate)- What are the main steps in hypothesis testing?
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State hypotheses, choose significance level, compute test statistic, determine p-value, make decision
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