K-Nearest Neighbors algorithm (KNN) K-Nearest Neighbors algorithm (KNN) is a very important supervised machine learning algorithm and one should start from this algorithm. It is easy to understand compare to other algorithms and does not involve complex mathematical concepts. In this post, I will explain k-Nearest Neighbors algorithm using Irish flowers data set. From […]
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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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Group in Algebra Let G be a non-empty set and * (multiplication) be a binary operation defined on G. Then algebraic structure (G, *) is called group if it satisfies the following axioms. 1- Closure property If a∈G, and b∈G then a*b∈G it is called closure property. of G 2- Associativity If a∈G, b∈G ,
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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1-Random Experiment- If an experiment is conducted then the outcome will not be unique but it may be from possible list of outcomes. Example- If you are tossing two coins the possible outcomes would be {TT, TH, HT,HH}. 2- Events- Outcome of a random experiment is called events, if you are tossing two coins then
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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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