Module Three: Anticipating Patterns
Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable Combining i..
Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable Combining i..Bayes Theorem, Binomial and Poisson Distributions
Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..
Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..Binomial Distribution
Binomial Distribution - A trial, which has only two outcomes i.e., "a success" or "a failure", is called a Bernoulli trial. Let X be the number of successes in a Bernoulli trial, then X can take 0 or 1 and P(X =1) = p = "probability of a success" P(X = 0) = 1 - p = q = "probability of fai..
Theorem:
The number of circular permutations of n different objects is (n-1)..
Theorem:
The number of permutations of n dissimilar things taken r ..
The number of permutations of n dissimilar things taken r ..Theorems of Probability
Theorem 1:(Addition Rule of Probability) - If A and B are any two events, th..
Theorem 1:(Addition Rule of Probability) - If A and B are any two events, th..Baye's Theorem
In the previous section, we have learnt that i) If A and B are two mutually exclusive events, then ii) Before we state and prove Baye's Theorem, we use the above two rules to state the law of total probability. The law of total probability is useful in proving Baye's theorem and..
In the previous section, we have learnt that i) If A and B are two mutually exclusive events, then ii) Before we state and prove Baye's Theorem, we use the above two rules to state the law of total probability. The law of total probability is useful in proving Baye's theorem and..Theorems of Probability 1. Addition Rule of Probability: If A and B are any two events, then 2. P(A C ) = 1 - P(A). 3. P( f ) = ..
1. Addition Rule of Probability: If A and B are any two events, then 2. P(A C ) = 1 - P(A). 3. P( f ) = ..Baye's Theorem
Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i ) 0 for all i. Then for any event A which is a subset of We hav..
Let S be a sample space. If A 1 , A, A 3 ... A n are mutually exclusive and exhaustive events such that P(A i ) 0 for all i. Then for any event A which is a subset of We hav..Poisson Distribution as a Limiting Form of the Binomial Distribution
We shall now deduce the Poisson distribution from the binomial distribution by assuming that n and p 0 such that the product np always remains finite, say l . We shall now use a very important result of limits in Calcu..
We shall now deduce the Poisson distribution from the binomial distribution by assuming that n and p 0 such that the product np always remains finite, say l . We shall now use a very important result of limits in Calcu..See what our Users say :
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