Bernoulli Trials Many experiments have only two outcomes, for example if you are tossing a coin you will get head or tail. If you rolling a dice you will have number on the face which may be an even or an odd number. When a company manufactures items, so item may be defective or it […]
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Random variable is a very important concept in probability, statistics, data science and machine learning, one must learn concept of random variable and related concepts. In this post, I have explained random variable and probability mass function that will help you to have basic understanding of random variable and probability mass function. To understand random
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Population- Population refers to group of individuals under study, you can understand it by an example. Suppose you have a pharmacy company and it has made a new drug and you want see the effect of the drug on the people of country. Here whole people of country are population for your study. Sample- Reality
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Covariance and Correlation- Covariance and correlation both measure linear relationship between two variables. However, they differ at some points. In this post I will explain covariance and correlation and how they differ from each other. Covariance between two variables is written as Cov(X,Y) and is defined as Calculation of Covariance If you look at the
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Variance of a Continuous Random Variable If X is a random variable having mean μ , then variance of random variable X is denoted as Var(X) and read as variance of X and defined as. Var(X)=E[(X-μ)²] Where Variance of a random variable measures dispersion, that means how for values spread out from mean or expected
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Expectation of a Continuous Random Variable Expectation of a continuous random variable is defined as Suppose a continuous random variable X is uniformly distributed on [a, b]. Density function of uniformly distributed random variable X is Expectation of uniformly distributed random variable X is See Video See Also: Expectation in Statistics Expectation of a Discrete
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Mathematical or Classical Probability- If a random experiment is conducted which results in n exhaustive, mutually exclusive, and equally likely outcomes and there are m favorable cases of occurrence of an event E. Then probability of happening event E is P(E)=m/n Suppose you are tossing a coin and want to get probability of getting head
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Joint and Marginal Probability Mass Function For UploadingIf (X,Y) is a two-dimensional discrete random variable, then joint probability mass function of X and Y denoted by pxy and is defined as pxy(xi,yj)=P(X=xi,Y=yj) If you toss three coins the following sample space you will get. S={TTT, TTH, THT, THH, HTT, HTH, HHT,HHH} X—- Occurrence of heads
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Entropy of a random variable measures uncertainty inherent to possible outcomes of the variable. H(X)= -Σin pilog2pi , where i=1, 2, 3 , 4, …..,n Where pi are probabilities of associated events. Take an example of tossing two coins, then you will have sample space . S={T,H} And X is defined as number of
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A random variable X is a function from a sample S to real numbers R, i.e X: S——>R. Suppose you are tossing three coins then the sample space would be. S={HHH,TTH, THT, THH, HTT, HTH, HHT, HHH} Then X maps sample space to real numbers. Where you can see that R={0,1,2, 3} You can also
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