## Knowledge in Maths

How to find the mean of the probability distribution: Steps

How to find the mean of the probability distribution: StepsStep 1: Convert all the percentages to decimal probabilities. For example: ...Step 2: Construct a probability distribution table. ...Step 3: Multiply the values in each column. ...Step 4: Add the results from step 3 together.

KEY TAKEAWAYS OF PROBABILITY DISTRIBUTION-

KEY TAKEAWAYS OF PROBABILITY DISTRIBUTION-A probability distribution depicts the expected outcomes of possible values for a given data generating process.Probability distributions come in many shapes with different characteristics, as defined by its mean, standard deviation, skewness, and kurtosis.Investors use probability distributions to anticipate returns on assets such as stocks over time and to hedge their risk.

Types of Probability Distributions

Types of Probability DistributionsThere are many different classifications of probability distributions. Some of them include the normal distribution,&nbsp;chi square istribution,&nbsp;binomial distribution and Poisson distribution. The different probability distributions serve different purposes and represent different data generation processes. The binomial distribution, for example, evaluates the probability of an event occurring several times over a given number of trials and given the event's probability in each trial. and may be generated by keeping track of how many free throws a basketball player makes in a game, where 1 = a basket and 0 = a miss. Another typical example would be to use a fair coin and figuring the probability of that coin coming up heads in 10 straight flips. A binomial distribution is&nbsp;discrete, as opposed to continuous, since only 1 or 0 is a valid response.The most commonly used distribution is the normal distribution, which is used frequently in finance, investing, science, and engineering. The normal distribution is fully characterized by its mean and standard deviation, meaning the distribution is not skewed and does exhibit kurtosis. This makes the distribution symmetric and it is depicted as a bell-shaped curve when plotted. A normal distribution is defined by a mean (average) of zero and a standard deviation of 1.0, with a skew of zero and kurtosis = 3. In a normal distribution, approximately 68 percent of the data collected will fall within +/- one standard deviation of the mean; approximately 95 percent within +/- two standard deviations; and 99.7 percent within three standard deviations. Unlike the binomial distribution, the normal distribution is continuous, meaning that all possible values are represented (as opposed to just 0 and 1 with nothing in between).Probability Distributions Used in InvestingStock returns are often assumed to be normally distributed but in reality, they exhibit kurtosis with large negative and positive returns seeming to occur more than would be predicted by a normal distribution. In fact, because stock prices are bounded by zero but offer a potential unlimited upside, the distribution of stock returns has been described as&nbsp;log normal. This shows up on a plot of stock returns with the tails of the distribution having greater thickness.Probability distributions are often used in risk management as well to evaluate the probability and amount of losses that an investment portfolio would incur based on a distribution of historical returns. One popular risk management metric used in investing is value-at-risk (VaR). VaR yields the minimum loss that can occur given a probability and time frame for a portfolio. Alternatively, an investor can get a probability of loss for an amount of loss and time frame using VaR. Misuse and overreliance on&nbsp;var has been implicated as one of the major causes of the 2008 financial crisis.Example of a Probability DistributionAs a simple example of a probability distribution, let us look at the number observed when rolling two standard six-sided dice. Each die has a 1/6 probability of rolling any single number, one through six, but the sum of two dice will form the probability distribution depicted in the image below. Seven is the most common outcome (1+6, 6+1, 5+2, 2+5, 3+4, 4+3). Two and twelve, on the other hand are far less likely (1+1 and 6+6).

Statistics

What Are Statistics?Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data. Some statistical measures include the following:MeanSkewnessKurtosisVarianceAnalysis of variance

Understanding Statistics

Understanding StatisticsStatistics is a term used to summarize a process that an analyst uses to characterize a data set. If the data set depends on a sample of a larger population, then the analyst can develop interpretations about the population primarily based on the statistical outcomes from the sample. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form.Statistics is used in various disciplines such , business, physical and social sciences, humanities, government, and manufacturing. Statistical data is gathered using a sample procedure or other method. Two types of statistical methods are used in analyzing data: descriptive statistics and inferential statistics. Descriptive statistics are used to synopsize data from a sample exercising the mean or standard deviation. Inferential statistics are used when data is viewed as a subclass of a specific population.

KEY TAKEAWAYS of statistics

KEY TAKEAWAYSStatistics studies methodologies to gather, review, analyze, and draw conclusions from data.There are many different types of statistics pertaining to which situation you need to analyze.Statistics are used to make better-informed business decisions

Types of Statistics

Types of StatisticsStatistics is a general, broad term, so it's natural that under that umbrella there exist a number of different models.MeanA mean is the mathematical average of a group of two or more numerals. The mean for a specified set of numbers can be computed in multiple ways, including the arithmetic mean, which shows how well a specific commodity performs over time, and the geometric mean, which shows the performance results of an investorâ€™s portfolio invested in that same commodity over the same period.Regression AnalysisRegression analysis determines the extent to which specific factors such as interest rates, the price of a product or service, or particular industries or sectors influence the price fluctuations of an asset. This is depicted in the form of a straight line called linear regression.SkewnessSkewness describes the degree a set of data varies from the standard distribution in a set of statistical data. Most data sets, including commodity returns and stock prices, have either positive skew, a curve skewed toward the left of the data average, or negative skew, a curve skewed toward the right of the data average.KurtosisKurtosis measures whether the data are light-tailed (less outlier-prone) or heavy-tailed (more outlier-prone) than the normal distribution.&nbsp;Data sets with high kurtosis have heavy tails, or outliers, which implies greater investment risk in the form of occasional wild returns. Data sets with low kurtosis have light tails, or lack of outliers, which implies lesser investment risk.VarianceVariance is a measurement of the span of numbers in a data set. The variance measures the distance each number in the set is from the mean. Variance can help determine the risk an investor might accept when buying an investment.Ronald Fisher developed the analysis of variance method. It is used to decide the effect solitary variables have on a variable that is dependent. It may be used to compare the performance of different stocks over time.

Variables

Variables&nbsp;are used to store information to be referenced and manipulated in a computer program. They also provide a way of labeling data with a descriptive name, so our programs can be understood more clearly by the reader and ourselves. It is helpful to think of variables as containers that hold information. Their sole purpose is to label and store data in memory. This data can then be used throughout your program.

Naming variables