Variance and Standard Deviation are both essential concepts in statistics and finance. Let’s explore the differences between them: Variance: Definition: Variance is a numerical value that describes the variability of observations from their arithmetic mean. Calculation: To find the variance, calculate the squared differences between each data point and the mean, then average these squared […]
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Suppose you want to solve an equation x2+1=0 then you will get x=√-1 which does not belongs to real number system. Leonhard Euler proposed to write √-1 as i (iota) and gave concept of complex numbers. Integral Power of i (iota) i2=-1, i3=-i, i4=1 i5=i, i6=-1, i7=-1, i8=1
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A function is called identity function if its domain and range is set of real numbers i.e f:R–>R and is defined as f(x)=x. Further, in the below image you can see for every value of x , f(x) has the same value. In the graph, you can see a straight which passes through origin.
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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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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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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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Taylor’s theorem states that we can get expansion of a function f(x) at x=a This can be written as When we put a=0 it becomes Maclaurin’s series, and it has a lot of applications in mathematics and other areas. If you want expansion of ex you will require to find f(0), f’(0), f’’(0), f’’’(0), ………….,
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