Calculate the mean, and the variance of the following probability density functions:
i) Uniform , and
elsewhere.
ii) Rayleigh distribution
Let's calculate the mean and variance for both distributions numerically. --- ### (i) Uniform Distribution The probability density function (PDF) of a uniform distribution between \(-a\) and \(a\) is: \[ p(x) = _____ _______ _______ ________ _________ __________ _____ ___.
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State Ising model and obtain the partition function (In Z) for 1D in the absence of an external magnetic field up to second order perturbation. Explain the physical significance of each term in the Hamiltonian and discuss the role of the coupling constant J.
Calculate the mean, and the variance of the following probability density functions:
i) Uniform , and
elsewhere.
ii) Rayleigh distribution
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