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How are the probabilities of a random variable determined?
All random variables (discrete and continuous) have a cumulative distribution function.It is a function giving the probability that the random variable X is less than or equal to x, for every value x.For a discrete random variable, the cumulative distribution function is found by summing up the probabilities.
How to find the probability of one variable being greater than another?
In general, suppose X has distribution function G ( x), and Y has distribution function H ( x) and X and Y are independent. We need to find the probability P ( X > Y).
How are X and Y independent random variables?
Conversely, X and Y are independent random variables if for all x and y, their joint distribution function F(x, y) can be expressed as a prod- uct of a function of xalone and a function of yalone (which are the marginal distributions of andX Y, respec- tively).
What is the probability that X is less than or equal to 2?
The probability that X is less than or equal to 1 is 0.1, the probability that X is less than or equal to 2 is 0.1+0.3 = 0.4, the probability that X is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and the probability that X is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.
How is the cumulative distribution function of a random variable found?
All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable Xis less than or equal to x, for every value x. For a discrete random variable, the cumulative distribution function is found by summing up the probabilities.
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.
What do you call a random variable that takes on infinite values?
A random variable that takes on a finite or countably infinite number of values (see page 4) is called a dis- crete random variable while one which takes on a noncountably infinite number of values is called a nondiscrete random variable.