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 […]
Definition of Probability Read More »
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
Expectation of a Discrete Random Variable Read More »
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
Random Variable and Probability Density Function Read More »