Ray Vickson said:No wonder you are having trouble: you are 100% wrong in what you are writing. Go back and apply known results correctly.
RGV
magnifik said:For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and n
I know that for the sum of independent rv's the PMF is a convolution
so...
Ʃ(1/k)(1/n-k) from k = 1 to n
PMF (Probability Mass Function) for the sum of random variables is a mathematical concept that describes the probability distribution of the sum of two or more random variables. It is a useful tool in probability theory and statistics for understanding the likelihood of certain outcomes when multiple random variables are involved.
The PMF for the sum of random variables is calculated by convolving the individual PMFs of the random variables. This involves multiplying the probabilities of each possible outcome for one variable with the probabilities for each possible outcome of the other variable, and then summing these values to get the overall probability for each possible sum.
PMF for a single random variable describes the likelihood of each possible outcome for that variable, while PMF for the sum of random variables describes the likelihood of each possible sum of two or more variables. Additionally, PMF for the sum of random variables takes into account the probabilities of all possible combinations of outcomes for the individual variables, while PMF for a single random variable only considers the probabilities for that one variable.
PMF for the sum of random variables is useful in situations where multiple random variables are involved and there is interest in understanding the likelihood of different combinations of outcomes. It is commonly used in fields such as finance, engineering, and epidemiology to model complex systems and make predictions about possible outcomes.
One limitation of PMF for the sum of random variables is that it can become computationally complex and difficult to calculate for large numbers of variables. Additionally, it assumes that the individual variables are independent, which may not always be the case in real-world scenarios. Finally, PMF for the sum of random variables is only applicable to discrete random variables and cannot be used for continuous variables.