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nikozm
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Hello,
I 'm trying to express the PDF of z (z ≥ 0) where z = x-y (and let x,y ≥ 0)
Thank you in advance
I 'm trying to express the PDF of z (z ≥ 0) where z = x-y (and let x,y ≥ 0)
Thank you in advance
nikozm said:Thank you for your answer.
I 'm trying to express the distribution of x-y in integral form. I m not sure about the integration bounds though.
I presume that the standard convolution PDF can be used: let z= x-y, then:
fz(z) =∫ fx(x)*fy(z+x) dx, but with what integration lower and upper bounds ??
Assume that x,y ≥ 0.
Any help would be useful
The PDF (probability density function) of z where z = x-y is the mathematical representation of the likelihood of obtaining a certain value of z, given the values of x and y. It describes the relative frequency of different values of z and can be represented by a graph or an equation.
The PDF of z is calculated by taking the derivative of the cumulative distribution function (CDF) of z. This derivative is also known as the probability density function and it measures the rate of change of the CDF at a specific value of z.
The CDF of z is the integral of the PDF of z. In other words, the CDF represents the area under the PDF curve up to a certain value of z. The PDF and CDF are both used to describe the probability distribution of a random variable and are closely related to each other.
The shape of the PDF of z can be affected by various factors, such as the mean and standard deviation of the underlying distribution of x and y, the correlation between x and y, and the sample size. Changes in these factors can result in a shift, skew, or change in the overall shape of the PDF.
The PDF of z is used in statistical analysis to determine the likelihood of obtaining a certain value of z in a given dataset. It is also used to calculate probabilities and make predictions based on the distribution of z. Additionally, the PDF is used to compare different distributions and understand the relationship between different variables.