bl00d said:If X is a continuous random variable and g is a continuous function
defined on X (Ω), then Y = g(X ) is a continuous random variable.
Prove or disprove it.
A continuous random variable is a type of random variable where the possible values it can take on are infinite and uncountable. This means that the variable can take on any value within a specific range, rather than discrete values like in a discrete random variable.
The process for proving Y=g(X) as a continuous random variable involves showing that the function g(X) is continuous and that the random variable X is also continuous. This can be done through mathematical proofs or by using the definition of a continuous random variable and its properties.
Proving Y=g(X) as a continuous random variable is important in statistics and probability, as it allows for the use of continuous probability distributions to model and analyze real-world phenomena. This allows for more accurate predictions and better understanding of the underlying processes.
No, Y=g(X) can only be a continuous random variable if both Y and X are continuous. If X is not continuous, then there will be gaps in the possible values of Y and it cannot be considered a continuous random variable.
Some examples of Y=g(X) as a continuous random variable include the normal distribution, exponential distribution, and beta distribution. These probability distributions are commonly used to model continuous variables such as height, weight, and time.