Mathematical Methods Β· Unit 4 Β· Continuous random variables and the normal distribution Β· General continuous random variables

Calculate the expected value, 𝐸 (𝑋) = πœ‡ = ∫ π‘₯𝑝(π‘₯) 𝑑π‘₯ ∞ βˆ’βˆž, of a continuous random variable where 𝑝(π‘₯) is the probability density function.

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Calculate the variance, π‘‰π‘Žπ‘Ÿ (𝑋) = 𝜎 2 = ∫ (π‘₯ βˆ’ πœ‡) ∞ βˆ’βˆž 2 𝑝(π‘₯)𝑑π‘₯, and standard deviation 𝜎, of a continuous random variable.
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