lanedance said:start with an easier problem first
Y = X1 & X2
it you're still getting no where, try looking up convolutions
A PDF (Probability Density Function) is a mathematical function that describes the probability of a random variable taking on a certain value. It is used to model continuous random variables.
A continuous uniform random variable is a type of random variable where every value within a certain range has an equal chance of being chosen. This type of random variable follows a uniform distribution and is commonly used in modeling real-world scenarios.
The PDF of the sum of three continuous uniform random variables is calculated by convolving the individual PDFs of each variable. This involves finding the sum of the individual variables and then integrating the resulting function to get the final PDF.
Yes, the PDF of the sum of three continuous uniform random variables can be simplified by using the convolution theorem. This theorem states that the Fourier transform of the sum of two functions is equal to the product of their individual Fourier transforms. By applying this theorem, the convolution integral can be simplified to a simple multiplication of the individual Fourier transforms.
The PDF of the sum of three continuous uniform random variables is used in various fields, such as engineering, physics, and economics, to model and analyze real-world data. It helps in understanding the distribution of a variable and predicting the likelihood of certain outcomes. This information can then be used to make informed decisions and optimize processes.