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# Probability Distribution

## What is Meant by Probability Distribution?

A probability distribution refers to a statistical function defining all the possible values and probabilities that a random variable will take within a given range. This range is bounded between the minimum and maximum possible values.

Still, it depends on a variety of variables precisely where the potential value is likely to be calculated from the probability distribution.

These variables include the mean (average) distribution, standard deviation, skewness, and kurtosis.

## How Does the Probability Distribution Function?

Probably, the most common probability distribution is the normal distribution, or "bell curve," though there are several commonly utilised distributions. Usually, any phenomenon's method of producing data can determine its probability distribution. The process is known as the probability density function.

Probability distributions can also be applied to construct cumulative distribution functions (CDFs), taking the cumulative probability of occurrences, always beginning at zero and ending at 100%.

Academics, financial analysts, and fund managers will calculate the probability distribution of a given stock to assess the potential expected returns the stock can produce in the future. The history of a stock's returns, measured for any time interval, is likely to consist of only a fraction of the returns from the stock, which will subject the study to sampling error. This error can be drastically reduced by increasing the sample size.

Let us look at the number observed when rolling two regular six-sided dice, as a basic example of a probability distribution. Every die has a 1/6 chance of rolling any single number, one through six. Still, the sum of two dice will form the probability distribution. The most common outcome is the seven (1 + 6, 6 + 1, 5 + 2, 2 + 5, 3 + 4, 4 + 3). In comparison, two and twelve are much less probable (1 + 1 and 6 + 6).

Different kinds of a probability distribution can be classified. Many of them include the normal distribution, the Chi-square distribution, Poisson distribution, and the binomial distribution. The different probability distribution serves various purposes and represents different processes for generating data.

The probability distribution most widely used is the standard distribution, which is often used in banking, business, research, and engineering. The normal distribution is entirely characterised by its mean and standard deviation, meaning there is no distorted distribution and there is kurtosis.

## Application of Probability Distribution

Investors use probability distribution to predict returns overtime on assets, such as securities and to hedge their risk. Stock returns are often thought to be normally distributed. They show kurtosis with significant negative and positive returns. It appears to be more than a normal distribution would expect.

The distribution of stock returns has been defined as log-normal. It is because the stock prices are bounded by zero but give a possible unlimited upside. It shows up on a stock return plot with the distribution tails being larger in thickness.

Probability distributions are often commonly used in risk management to measure the probability. It also measures the sum of losses that an investment portfolio will experience based on a distribution of historical returns. One standard investment risk management metric is the Value-at-Risk (VaR). VaR yields the lowest loss that may occur, given a portfolio probability and time frame.

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