Abstract
This chapter introduces random variables and mathematical expectation. Discrete and continuous random variables and their basic properties are discussed. A simple technique to find the expectation of functions of random variables is given. This is followed by a discussion on moments (ordinary, central, factorial) and variance as expected values.
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Notes
- 1.
As the numerator unit is ml\(^3\) and denominator unit is a square, the units do not cancel out, so that CI is an absolute measure. This could be converted into a relative measure by dividing it by height.
- 2.
Borg’s category ratio-scale (CR-10) is a common scale used in medical sciences in which 0 indicates total absence, 0.5 = very very weak, 1 = very weak 2 = weak (light), 3 = moderate, 4 = somewhat strong, 5 = strong, 7 = very strong, 10 = very very strong (max).
- 3.
BMI values less than 15 indicates an unusual health condition in a patient. The lowest recorded BMI is 6.7 (see https://pubmed.ncbi.nlm.nih.gov/35569150/).
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Chattamvelli, R., Shanmugam, R. (2024). Mathematical Expectation. In: Random Variables for Scientists and Engineers. Synthesis Lectures on Engineering, Science, and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-58931-7_1
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