dexterdev said:Hi all,
I would like to make things clear about the notations used in probability. what does X and x in pdf
f[itex]_{X}[/itex](x) means.
-Devanand T
The uppercase X designates the random variable. The lowercase x designates some particular value of the random variable.dexterdev said:Hi all,
I would like to make things clear about the notations used in probability. what does X and x in pdf
f[itex]_{X}[/itex](x) means.
No, it doesn't mean "whatever the person who wrote it decides that it means", and it's best not to guess when you don't know the answer. Suppose you're reading up on chemistry and you come across H2O. This doesn't mean whatever the author intended. It has a very specific meaning. It's water. Similarly, the nomenclature [itex]f_X(x)[/itex] is widely used to mean the probability density function or probability mass function for some random variable [itex]X[/itex]. That nomenclature is standard, just as is H2O.ImaLooser said:Well, it means whatever the person who wrote it decides that it means. I would guess that fX() is a random function, and x is some sort of value. Like fX(x) could be equal to x + X.
Probability is a measure of the likelihood that a certain event will occur. It is a numerical value between 0 and 1, where 0 represents impossibility and 1 represents certainty. On the other hand, likelihood is a measure of how well a particular probability model fits the observed data. It is also a numerical value between 0 and 1, but it does not represent the actual probability of an event occurring.
Discrete probability distributions are used for situations where the random variable can only take on a finite or countably infinite number of values. Examples include flipping a coin or rolling a die. Continuous probability distributions, on the other hand, are used for situations where the random variable can take on any value within a certain range. Examples include measuring the height or weight of a person.
To calculate the probability of independent events, you simply multiply the probabilities of each event occurring. For example, if event A has a probability of 0.6 and event B has a probability of 0.4, the probability of both events occurring is 0.6 x 0.4 = 0.24. This is known as the multiplication rule for independent events.
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are two events. Joint probability, on the other hand, is the probability of two events occurring together. It is denoted as P(A and B) or P(A ∩ B). Conditional and joint probabilities are related through the conditional probability formula, P(A|B) = P(A and B)/P(B).
A probability distribution function (PDF) is a mathematical function that describes the probabilities of all possible outcomes of a random variable. The area under the PDF curve represents the probability of the random variable falling within a certain range of values. The height of the curve at a particular point represents the probability density at that point. In other words, the PDF shows the relative likelihood of each possible outcome occurring.