Find the probability of 3 successes in 3 trials, if the probability of..
Find the probability of 3 successes in 3 trials, if the probability of success on each trial is 0.8. => 0.832 or 0.48 or 0.163 or 0.512..
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..
Summary
1. If x is a discrete random variable assuming the values x 1 , x 2 , x 3 ,.,x n with probabilities p 1 , p 2 , p 3 ,., p n respectively then (x 1 ,p 1 ), (x 2 , p 2 ),(x n , p n ) defines a probability distribution of X. 2. Let n independent be..
Bernoulli trial:
A random experiment which has only two outcomes (success or failure) Let n independent bernoulli trials be performed and X denote the number of successes in n trials then X follows a binomial distribution. The probability of success b..
A random experiment which has only two outcomes (success or failure) Let n independent bernoulli trials be performed and X denote the number of successes in n trials then X follows a binomial distribution. The probability of success b..Poisson Distribution
Poisson distribution is a limiting process of binomial distribution. Poisson distribution occurs when there are events which do not occur as outcomes of a definite number of outcomes. Poisson distribution is used under the following conditions: Number of trials n tends to infinity Pr..
Poisson distribution is a limiting process of binomial distribution. Poisson distribution occurs when there are events which do not occur as outcomes of a definite number of outcomes. Poisson distribution is used under the following conditions: Number of trials n tends to infinity Pr..Example:
5 cards are drawn successively with replacement from well shuffled deck of 52 cards. What is the probability that i) all the five cards are spades ii) only 3 cards are spades iii) none is a spa..
Note:
Each element of S denotes a possible outcome. Each element of S is known as sample point. Any trial results in an outcome and corresponds to one and only one element of the set S. e.g., 1. In the experiment of tossing a coin, S = {H, T} 2. In the experiment of tossing two coins sim..
Summary
The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The prin..
Note 3:
Although the probability distribution of a continuous random variable cannot be presented in tabular form, it can have a formula in the form of a function represented by f(x) usually called the probability density functio..
Question 3
Question: The median of the first ten prime numbers. Answer: The first 10 prime numbers ={2, 3, 5, 7, 11, 13, 17, 19, 23, 29} ..
Question: The median of the first ten prime numbers. Answer: The first 10 prime numbers ={2, 3, 5, 7, 11, 13, 17, 19, 23, 29} .. Result
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