The probability mass function (pmf, you should know this) of the Poisson distribution is
p(x)=((e-λ)*λx)/(x!), where x= 0, 1, ........
Then you take the expected value of exp(tx), you should always keep in mind to find the moment generating function (mgf) you must always do
(etx)*p(x), where t is a random variable
Therefore,
(etx)*((e-λ*λx)/(x!))
(e-λ)*sum[(e-λ*λx)/(x!)]
Thee-λ is only a constant; thus, it can be pulled out of the sums.
Continuing,
(e-λ)*sum[(λ*et)x)/x!]
Let y=λ*et
(e-λ)*sum[(y)x/x!]
By Macalurins series, the sum[(yx)/x! ]= ey
Soonwards
(ey)*(e-λ)
Lets return the y by λ*et
var(X) = (xm/a - 1)2 a/a-2 . If a < or equal to 2, the variance does not exist.
Derive the S matrix for E-plane Tee
reconvene
Classic IB student...
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(1/x)e^-(y/x)
The moment generating function for any real valued probability distribution is the expected value of e^tX provided that the expectation exists.For the Type I Pareto distribution with tail index a, this isa*[-x(m)t)^a*Gamma[-a, -x(m)t)] for t < 0, where x(m) is the scale parameter and represents the least possible positive value of X.
In statistics, the ogive curve is an approximation to the cumulative distribution function. It can be used to obtain various percentiles quickly as well as to derive the probability density function.
ref veeru
The mode of the Pareto distribution is its lowest value.
To derive the mean of generalized Pareto distribution you must be good with numbers. You must be good in Calculus, Algebra and Statistics.
1) What is the definition of dielectric permittivity on the basis of Maxwell equations? 2) What is Poisson equation of Electrostatics? Derive the Poisson equation from Maxwell equations. 3) Write the Biot-Savar equation. What is the meaning? 4) Derive a wave equation of a plain electromagnetic wave from Maxwell equation.
derive cost function from production function mathematically, usually done by utilizing mathematical optimization methods.
The total deviation from the mean for ANY distribution is always zero.
Here is the derivation on dsplog: http://www.dsplog.com/2008/07/17/derive-pdf-rayleigh-random-variable/
Here is qn excellent article that explains step by step: http://MasteringElectronicsDesign.com/how-to-derive-the-instrumentation-amplifier-transfer-function/
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