A discrete probability distribution is defined over a set value (such as a value of 1 or 2 or 3, etc). A continuous probability distribution is defined over an infinite number of points (such as all values between 1 and 3, inclusive).
Probability is the chance of some outcome while actuality is the realistic chance and actual outcome of an event.
the normal distribution is a bell shape and expeonential is rectangular
Logit and probit models are statistical techniques used for modeling binary outcome variables, where the response can take one of two possible values (e.g., success/failure). The logit model uses a logistic function to model the probability of an event occurring, while the probit model employs the cumulative distribution function of the standard normal distribution. Both models estimate the relationship between independent variables and the probability of the dependent variable being one of the outcomes, but they differ in their underlying assumptions and mathematical formulations. These models are commonly used in fields such as economics, sociology, and biomedical research for classification and prediction tasks.
Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.
No, a distribution can have infinitely many moments: the first is the mean, the second variance. Then there are skewness (3), kurtosis (4), hyperskewness (5), hyperflatness (6) and so on.If mk represents the kth moment, thenmk = E[(X - m1)k] where E is the expected value.It is, therefore, perfectly possible for m1 and m2 to be the same but for the distribution to differ at the higher moments.
The normal distribution and the t-distribution are both symmetric bell-shaped continuous probability distribution functions. The t-distribution has heavier tails: the probability of observations further from the mean is greater than for the normal distribution. There are other differences in terms of when it is appropriate to use them. Finally, the standard normal distribution is a special case of a normal distribution such that the mean is 0 and the standard deviation is 1.
A continuous system is described by equations that account for variations in state variables across a continuous domain, often using partial differential equations (PDEs) to represent phenomena like wave propagation or heat distribution. In contrast, a discrete system is characterized by equations that describe state variables at distinct points or intervals, typically using ordinary differential equations (ODEs) or difference equations. This fundamental difference reflects how continuous systems model interactions over a continuum, while discrete systems focus on specific, isolated events or states.
In optimization, a discrete problem involves variables that can take on distinct, separate values, often represented as integers, such as scheduling or routing problems. In contrast, a continuous problem allows variables to take on any value within a given range, often represented by real numbers, such as minimizing a function over a continuous domain. Consequently, the optimization techniques differ; discrete problems typically use methods like integer programming or combinatorial optimization, while continuous problems often employ techniques like gradient descent or linear programming.
Probability/ Statistics
Aristotle believed matter was continuous and unchanging, while scientists view matter as composed of discrete particles and subject to change. Aristotle's concept of matter lacked the atomic nature described by scientists later on.
Probability is the chance of some outcome while actuality is the realistic chance and actual outcome of an event.
The standard normal distribution has a mean of 0 and a standard deviation of 1.
The spectra of daylight and fluorescent light differ primarily in their distribution of wavelengths. Daylight produces a continuous spectrum with a balanced range of wavelengths, including most colors of the visible spectrum, resulting in a natural and full-spectrum illumination. In contrast, fluorescent light emits a more discrete spectrum, characterized by distinct peaks at specific wavelengths due to the excitations of gas and phosphors, which can lead to a less balanced color rendering and sometimes a cooler appearance. This difference affects how colors are perceived under each type of light.
A continuous variable is one that can assume different values between each point. Put as an example (e.g when looking at height) one can assume a height of 178, 178.1, 178.2. . . 178.9. Thus continuous variables can be used when looking at time or length for example. Continuous variables will differ from discrete variables which assume a fixed value for example number of times you take a shower, how many cars you have or how many kids in a family. Values can not be specified as decimals (e.g. you can not have 1.2 cars or 2.7 kids in a family).
A continuous variable is one that can assume different values between each point. Put as an example (e.g when looking at height) one can assume a height of 178, 178.1, 178.2. . . 178.9. Thus continuous variables can be used when looking at time or length for example. Continuous variables will differ from discrete variables which assume a fixed value for example number of times you take a shower, how many cars you have or how many kids in a family. Values can not be specified as decimals (e.g. you can not have 1.2 cars or 2.7 kids in a family).
the normal distribution is a bell shape and expeonential is rectangular
Yes.