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seeker101
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Could someone point me to a book that has a proof of the above statement?
Thanks in advance!
Thanks in advance!
artbio said:Hi.
That statement seems obvious to me. I don't need a proof.
If you have two variables for which the outcome is uncertain i.e random. The outcome of their sum will also be uncertain i.e random. So the sum of two random variables is also a random variable. Don't you think? I don't even know if there is a written proof for that.
A random variable is a numerical quantity that takes on different values based on the outcome of a random event. It is a mathematical representation of the uncertain nature of events in a probabilistic system.
A regular variable takes on a specific value, while a random variable can take on a range of values based on the probability of certain outcomes. Random variables are also used to model uncertain or random phenomena, while regular variables are used in mathematical equations and formulas.
The sum of two random variables is a new random variable that represents the combined outcome of the two original variables. It takes on values based on the sum of the values of the two individual variables.
In order to prove that the sum of two random variables is also a random variable, we must show that it follows the properties of a random variable. This includes having a defined probability distribution, taking on numerical values, and being able to be manipulated in mathematical operations.
Real-world examples of the sum of two random variables include adding the outcomes of two dice rolls, combining the results of two medical tests, or calculating the total cost of two items with different prices. Essentially, anytime two uncertain quantities are combined, the result can be represented as the sum of two random variables.