LCKurtz said:You can do that. The expected value operator is linear.
The concept of "Probability = sum of n uniformly distributed r.v.'s" refers to the idea that the total probability of an event occurring is equal to the sum of the probabilities of each individual outcome within that event. This is often used in probability and statistics to calculate the likelihood of a certain outcome when multiple variables are involved.
To calculate the sum of n uniformly distributed random variables, you would first need to define the probability distribution of each variable. Then, you would use the formula for calculating the sum of independent random variables, which is the sum of their expected values. In the case of uniformly distributed variables, the expected value is equal to the average of the minimum and maximum values of the distribution.
Yes, the sum of n uniformly distributed random variables can be greater than 1. This is because the sum of probabilities can exceed 1 when the events are not mutually exclusive. In other words, there can be some overlap or intersection between the different outcomes being considered.
The concept of "Probability = sum of n uniformly distributed r.v.'s" is commonly applied in various fields such as finance, engineering, and social sciences. For example, it can be used to calculate the risk of a certain investment portfolio, predict the likelihood of an earthquake occurring in a certain area, or estimate the probability of a certain demographic group voting for a particular candidate in an election.
While the concept of "Probability = sum of n uniformly distributed r.v.'s" is widely applicable, there are some limitations to its use. One limitation is that it assumes that the variables are independent, meaning that the outcome of one does not affect the outcome of the others. It also assumes that the variables are distributed uniformly, which may not always be the case in real-life situations. Additionally, this concept may not be appropriate for more complex or non-linear relationships between variables.