P(A | conditional probability of event A given event B P(A | B) = 0.3 B) probability function occured probability density f (x) P(a x b) = f (x)dx ≤ ≤ ∫ function (pdf) cumulative F(x) distribution function F(x) = P(X≤ (cdf) μ population mean mean of population values μ = 10 E(X) expected value of random variable X E(X) = 10 E(X | conditional expected of random variable X E(X | Y=2) = 5 Y) expectation given Y var(X) variance of random variable X var(X) = 4 σ2 = 4 variance of population values σ2 standard deviation of random variable std(X) std(X) = 2 X standard deviation value of random σX = 2 σX variable X median middle of random variable x covariance of random variables X and covariance cov(X,Y) = 4 Y correlation of random variables X and correlation corr(X,Y) = 0.6 Y correlation of random variables X and ρX,Y correlation = 0.6 ρX,Y Y
P(A | B) conditional probability function probability of event A given event B occured P(A | B) = 0.3 f (x) probability density function (pdf) P(a ≤ x ≤ b) = ∫ f (x)dx F(x) cumulative distribution function (cdf) F(x) = P(X≤ μ population mean mean of population values μ = 10 E(X) expected value of random variable X E(X) = 10 E(X | Y) conditional expectation expected of random variable X given Y E(X | Y=2) = 5 var(X) variance of random variable X var(X) = 4 σ2 variance of population values σ2 = 4 std(X) standard deviation of random variable X std(X) = 2 σX standard deviation value of random variable X σX = 2 median middle of random variable x covariance covariance of random variables X and Y cov(X,Y) = 4 correlation correlation of random variables X and Y corr(X,Y) = 0.6 ρX,Y correlation correlation of random variables X and Y ρX,Y = 0.6
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