Search results
Results from the WOW.Com Content Network
This function is real-valued because it corresponds to a random variable that is symmetric around the origin; however characteristic functions may generally be complex-valued. In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.
Law of the unconscious statistician: The expected value of a measurable function of , (), given that has a probability density function (), is given by the inner product of and : [34] [()] = (). This formula also holds in multidimensional case, when g {\displaystyle g} is a function of several random variables, and f {\displaystyle f} is ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
Consider a case where n tickets numbered from 1 to n are placed in a box and one is selected at random, giving a value X. If n is unknown, then the maximum-likelihood estimator of n is X, even though the expectation of X given n is only (n + 1)/2; we can be certain only that n is at least X and is probably more.
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
Note that, as per the affine transformation property alluded to above, the utility function gives the same preferences orderings as does ; thus it is irrelevant that the values of and its expected value are always negative: what matters for preference ordering is which of two gambles gives the higher expected utility, not the numerical values ...
Although the concept of U-value (or U-factor) is universal, U-values can be expressed in different units. In most countries, U-value is expressed in SI units, as watts per square metre-kelvin: W/(m 2 ⋅K) In the United States, U-value is expressed as British thermal units (Btu) per hour-square feet-degrees Fahrenheit: Btu/(h⋅ft 2 ⋅°F)