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In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) [2] or occasionally P B (A).
Sometimes it really is, but in general it is not. Especially, Z is distributed uniformly on (-1,+1) and independent of the ratio Y/X, thus, P ( Z ≤ 0.5 | Y/X) = 0.75. On the other hand, the inequality z ≤ 0.5 holds on an arc of the circle x 2 + y 2 + z 2 = 1, y = cx (for any given c). The length of the arc is 2/3 of the length of the circle.
The function B(p,q) is the beta function. The parameter is the scale parameter and can thus be set to without loss of generality, but it is usually made explicit as in the function above. The location parameter (not included in the formula above) is usually left implicit and set to .
A real hyperelliptic curve of genus g over K is defined by an equation of the form : + = where () has degree not larger than g+1 while () must have degree 2g+1 or 2g+2. This curve is a non singular curve where no point (,) in the algebraic closure of satisfies the curve equation + = and both partial derivative equations: + = and ′ = ′ ().
Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters). [3]A tilde (~) denotes "has the probability distribution of". Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator of it, e.g., ^ is an estimator for .
z is the elevation in meters, R is the specific gas constant = 287.053 J/(kg K) T is the absolute temperature in kelvins = 288.15 K at sea level, g is the acceleration due to gravity = 9.806 65 m/s 2 at sea level, P is the pressure at a given point at elevation z in Pascals, and; P 0 is pressure at the reference point = 101,325 Pa at sea level.
The general form of wavefunction for a system of particles, each with position r i and z-component of spin s z i. Sums are over the discrete variable s z , integrals over continuous positions r . For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is ...
The real part of the invariant g 3 as a function of the square of the nome q on the unit disk. The imaginary part of the invariant g 3 as a function of the square of the nome q on the unit disk. The coefficients of the above differential equation g 2 and g 3 are known as the invariants.