The CDF value corresponds to the sum of the area under a normal distribution curve integration. The smaller the width of the panel the more accurate the integration will be.
3 The Normal Distribution
We will use a panel width of 00001.
. If the random variable is denoted by then it is also known as the expected value of denoted For a discrete probability distribution the mean is given by where the sum is taken over all possible values of the random variable and is the probability. A probability distribution is a mathematical description of the probabilities of events subsets of the sample spaceThe sample space often denoted by is the set of all possible outcomes of a random phenomenon being observed. In this figure the abscissa of the curve Cl represents the vertical stress 7 at different depths z below the center of a square area B x B which carries a surcharge g per unit area or a total surcharge load of B2q.
So we divide the whole area under the curve into small panels of a fixed width and we add up all those individual panels to get the total area under the curve. A set of real numbers a set of vectors a set of arbitrary non-numerical values etcFor example the sample space of a coin flip would be. The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution.
The abscissa of the curve C2 represents the corresponding stresses due to a concentrated load Q. It may be any set. This curve is obtained by the exact method explained under Sect.
Normal Distribution Principles
Normal Distribution
Normal Distribution
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