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What is the sample space of a continuous random variable?
The domain of a random variable is called a sample space, defined as the set of possible outcomes of a non-deterministic event. For example, in the event of a coin toss, only two possible outcomes are possible: heads or tails.
How do you write a continuous sample space?
A continuous sample space is based on the same principles, but it has an infinite number of items in the space. In other words, you can’t write out the space in the same way that you would write out the sample space for a die roll.
How is a sample space different from a random variable?
A sample space is a collection of all possible outcomes of a random experiment. A random variable is a function defined on a sample space. We shall consider several examples shortly. Later on we shall introduce probability functions on the sample spaces. A sample space may be finite or infinite.
Which is an example of a random variable?
A random variable is a function defined on a sample space. We shall consider several examples shortly. Later on we shall introduce probability functions on the sample spaces. A sample space may be finite or infinite. Infinite sample spaces may be discrete or continuous. Tossing a coin.
Which is an example of a sample space?
A sample space is the SET of values a random variable can take. You can think of random variable as an unopened box. This unopened box contains each member of the sample space with some probability. In your example of a dice roll, the sample space is {1,2,3,4,5,6}.
When is a random variable said to be continuous?
If the random variable X can assume an infinite and uncountable set of values, it is said to be a continuous random variable. When X takes any value in a given interval (a, b), it is said to be a continuous random variable in that interval. Formally, a continuous random variable is such whose cumulative distribution function is constant throughout.