Probability Distribution Assignment Help
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Probability Distribution: An Overview
Simply speaking, probability distribution is the possible outcomes in an experiment or survey, like in a toss with a coin, the two possible outcomes are head and tail. These possible outcomes are called sample space. A sample space may be numerical, non-numerical, or vector space.
Here are some important topics and definitions of Probability distribution –
Discrete random variable – If a fair coin is flipped four times, what would be all the possible outcomes and what would be the possibility of each outcome – these issues are solved with the help of discrete random variable.
Continuous Random variable – This defines a set of all possible values that are infinite in number and it is not possible to assign a probability to a particular outcome.
Normal Random variable – This is the most common form of continuous random variable. Graphically, it looks like a bell-shaped symmetric curve. The center point is called the mean value and is represented with a symbol µ (“mu”). The spread of the distribution on the two sides of the of the distribution curve is called standard deviation and represented with a symbol σ (“sigma”).
Cumulative distribution function – The cumulative distribution function (“c.d.f.“) of a continuous random variable X is defined as the value of the function x, when it varies within the range of {−∞ to +∞}.
Discrete probability distribution – A discrete probability distribution is defined as the probability of incidence of each value of a discrete random variable. With a discrete probability distribution, each probable value of the discrete random variable can be related with a non-zero probability. Thus, a discrete probability distribution is easily presentable in tabular form.
Continuous probability distribution – A continuous probability distribution describes all the possible values of continuous random variables.
Application of Probability Distribution
These days, very advanced form of software technologies, various models, functions and methodologies of probability distribution are frequently used in various business and scientific models. Uses of probability distribution have been proved to be very fruitful in those sectors where it is continuously used.
Probability distribution is quite important and widely used in actuarial science in the insurance and risk management. It is invariably used in different streams of physics, engineering, evolutionary biology, computer science, economics, business, medical science and psychiatry, etc. Probability distribution is more appropriate for modeling real-world complications in the above mentioned fields, where sudden changes in the variable factors are too common matter.
Related Topics of Probability Distribution
Beside the above mentioned topics, there are innumerable other important topics play crucial roles in probability distribution. Some of these topics are as follows –
- Binomial random variable
- Sampling distribution
- Confidence intervals
- Hypothesis testing
- ANOVA
- Comparing two groups
- Inference about regression
- Multiple linear regression
- Association between categorical variables
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