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  2. Integral bridge - Wikipedia

    en.wikipedia.org/wiki/Integral_bridge

    The omission of the expansion joint removes a pathway for the penetration of chloride-bearing road salts to the bridge's sub-structure. In the United Kingdom there is a presumption that most new short to medium length bridges will be of the integral type. [citation needed] An early example of an integral bridge is masonry arch bridge.

  3. Sum of normally distributed random variables - Wikipedia

    en.wikipedia.org/wiki/Sum_of_normally...

    Now, if a, b are any real constants (not both zero) then the probability that + is found by the same integral as above, but with the bounding line + =. The same rotation method works, and in this more general case we find that the closest point on the line to the origin is located a (signed) distance

  4. Conditional probability distribution - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability...

    Seen as a function of for given , (= | =) is a probability mass function and so the sum over all (or integral if it is a conditional probability density) is 1. Seen as a function of x {\displaystyle x} for given y {\displaystyle y} , it is a likelihood function , so that the sum (or integral) over all x {\displaystyle x} need not be 1.

  5. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ XY is near +1 (or −1). If ρ XY equals +1 or −1, it can be shown that the points in the joint probability distribution that receive positive probability fall exactly along a straight ...

  6. Characteristic function (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_function...

    The characteristic function of a real-valued random variable always exists, since it is an integral of a bounded continuous function over a space whose measure is finite. A characteristic function is uniformly continuous on the entire space. It is non-vanishing in a region around zero: φ(0) = 1. It is bounded: | φ(t) | ≤ 1.

  7. Copula (statistics) - Wikipedia

    en.wikipedia.org/wiki/Copula_(statistics)

    when joint probability density function between two random variables is known, the copula density function is known, and one of the two marginal functions are known, then, the other marginal function can be calculated, or

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  9. Discontinuity (geotechnical engineering) - Wikipedia

    en.wikipedia.org/wiki/Discontinuity...

    In geotechnical engineering, a discontinuity (often referred to as a joint) is a plane or surface that marks a change in physical or chemical characteristics in a soil or rock mass. A discontinuity can be, for example, a bedding , schistosity , foliation , joint , cleavage , fracture , fissure , crack, or fault plane.