A question in random variables and random processes

In summary, a random variable is a numerical value that can change based on chance and is denoted by a capital letter. There are two types: discrete, which has a countable number of values, and continuous, which can take on any value within a certain range. A probability distribution is a function that describes the likelihood of each possible outcome of a random variable. A random process is a mathematical model that describes the evolution of a system over time in a probabilistic manner. There are two types: stationary, which has constant statistical properties, and non-stationary, which has changing statistical properties. Stationary processes are easier to analyze and model than non-stationary processes.
  • #1
Shloa4
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I will be grateful for some help here.
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  • #2
The phase is the random variable of interest. X and Y are functions of the phase.
The basic idea is that if A is a random variable and f a function of A, then
E(f(A))=∫f(a)dF(a), where F(a) = P(A≤a), the distribution function for A.
 

1. What is a random variable?

A random variable is a mathematical concept that represents a numerical value that is subject to change based on chance. It is often denoted by a capital letter, such as X or Y, and can take on different values depending on the outcome of a random experiment.

2. What is the difference between a discrete and continuous random variable?

A discrete random variable can only take on a countable number of values, while a continuous random variable can take on any value within a certain range. For example, the number of heads in a coin toss is a discrete random variable, while the height of a person is a continuous random variable.

3. What is a probability distribution?

A probability distribution is a mathematical function that describes the likelihood of each possible outcome of a random variable. It can be represented graphically as a histogram or a line graph, and is used to calculate probabilities and make predictions about the outcomes of random experiments.

4. What is a random process?

A random process is a mathematical model that describes the evolution of a system over time in a probabilistic manner. It involves a collection of random variables that change over time, and is often used to study phenomena such as stock prices, weather patterns, and communication signals.

5. What is the difference between a stationary and non-stationary random process?

A stationary random process is one whose statistical properties, such as mean and variance, remain constant over time. On the other hand, a non-stationary random process has statistical properties that change over time. This could be due to external factors, trends, or seasonality. Stationary processes are often easier to analyze and model compared to non-stationary processes.

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