Distribution function and random variable

In summary, a distribution function, also known as a cumulative distribution function (CDF), is a mathematical function that describes the probability of a random variable taking on a certain value or falling within a certain range of values. A random variable is a numerical quantity whose value is determined by the outcome of a random event. It can take on different values with certain probabilities, and its behavior can be described by a probability distribution. There are two types of random variables: discrete, which can only take on a finite or countably infinite number of values, and continuous, which can take on any value within a certain range. The mean of a probability distribution, denoted by μ, is the average value of a random variable over many trials, while the expected
  • #1
PainterGuy
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Hi,

I cannot figure out how they got Table 2.1. For example, how come when x=1, F_X(x)=1/2? Could you please help me with it?

prob_11.jpg

Hi-resolution copy of the image: https://imagizer.imageshack.com/img923/2951/w9yTCQ.jpg
 
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  • #2
You count four elements there in the table, OK ? So it is 4/8=1/2.
 
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FAQ: Distribution function and random variable

What is a distribution function?

A distribution function, also known as a cumulative distribution function (CDF), is a mathematical function that describes the probability that a random variable takes on a certain value or falls within a certain range of values. It gives the cumulative probability of all values of the random variable up to a certain point.

What is a random variable?

A random variable is a variable whose value is determined by the outcome of a random process. It can take on a range of possible values, each with a certain probability of occurring. Random variables are used to model real-world phenomena that involve uncertainty or randomness.

How is a distribution function related to a probability distribution?

A distribution function is the mathematical representation of a probability distribution. It maps all possible values of a random variable to their corresponding probabilities. The area under the distribution function curve between two values represents the probability of the random variable falling within that range.

What are some common types of probability distributions?

There are many types of probability distributions, but some of the most commonly used include the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has its own unique shape and characteristics, and is used to model different types of random processes.

How are distribution functions used in statistics?

Distribution functions are essential in statistics because they allow us to calculate probabilities of events and make predictions based on data. They are used to analyze and interpret data, make inferences about populations, and test hypotheses. They are also used to generate random numbers for simulations and other statistical analyses.

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