kkirtac said:X1, X2, X3 are independent gaussian random variables.
Y1 = X1+X2+X3
Y2 = X1-X2
Y3 = X2-X3
are given. What is the joint pdf of Y1,Y2 and Y3 ?
A joint density function is a mathematical function that describes the probability of multiple random variables taking on specific values simultaneously. In other words, it shows the likelihood of two or more events occurring together.
A joint density function takes into account the probabilities of multiple variables, while a single variable density function only considers the probability of one variable. In other words, a joint density function is a multivariate function, while a single variable density function is univariate.
A joint density function must satisfy three properties: it must be non-negative for all values of the variables, the integral over all possible values must equal 1, and it must be continuous everywhere except for a finite number of points.
The probability of an event occurring can be calculated by taking the integral of the joint density function over the region corresponding to that event. This integration can be done using calculus.
Yes, a joint density function can be used for any number of normal distributions. However, as the number of distributions increases, the calculations become more complex and may require advanced mathematical techniques.