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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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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In this post, I am going to explain how to attach a Servo motor with Arduino. I will explain about programming and how to connect Servo motor with Arduino. You will require to install Servo library for functioning of Servo motor #include <Servo.h> Servo s; int i = 0; void setup() { s.attach(9); } void
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