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In Binomial Distribution if n is infinitely large, the probability p of occurrence of event’ is close to _______ and q is close to _________
- a)0 , 1
- b)1 , 0
- c)1 , 1
- d)none
Correct answer is option 'A'. Can you explain this answer?
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In Binomial Distribution if n is infinitely large, the probability p o...
Binomial Distribution and Infinite n
Binomial Distribution is a probability distribution that describes the number of successes in a fixed number of independent trials. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q = 1-p.
As the number of trials, n, becomes infinitely large, there are some observations:
- The probability of occurrence of the event, p, approaches 0.
- The probability of non-occurrence of the event, q, approaches 1.
Explanation
When n is very large, the probability of occurrence of the event in each trial becomes very small. As a result, the total number of successes in the n trials will also be small. This means that the binomial distribution will be skewed towards 0.
As n approaches infinity, the binomial distribution approaches a normal distribution. In a normal distribution, the mean is equal to the probability of occurrence of the event, p. As the probability of occurrence of the event approaches 0, the mean also approaches 0.
Similarly, in a normal distribution, the standard deviation is equal to the square root of pq. As q approaches 1, the standard deviation also approaches 0. This means that the distribution becomes more and more concentrated around the mean.
Conclusion
In summary, as the number of trials, n, becomes infinitely large, the probability of occurrence of the event, p, approaches 0, and the probability of non-occurrence of the event, q, approaches 1. This makes the binomial distribution skewed towards 0 and more and more concentrated around the mean.
Binomial Distribution is a probability distribution that describes the number of successes in a fixed number of independent trials. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q = 1-p.
As the number of trials, n, becomes infinitely large, there are some observations:
- The probability of occurrence of the event, p, approaches 0.
- The probability of non-occurrence of the event, q, approaches 1.
Explanation
When n is very large, the probability of occurrence of the event in each trial becomes very small. As a result, the total number of successes in the n trials will also be small. This means that the binomial distribution will be skewed towards 0.
As n approaches infinity, the binomial distribution approaches a normal distribution. In a normal distribution, the mean is equal to the probability of occurrence of the event, p. As the probability of occurrence of the event approaches 0, the mean also approaches 0.
Similarly, in a normal distribution, the standard deviation is equal to the square root of pq. As q approaches 1, the standard deviation also approaches 0. This means that the distribution becomes more and more concentrated around the mean.
Conclusion
In summary, as the number of trials, n, becomes infinitely large, the probability of occurrence of the event, p, approaches 0, and the probability of non-occurrence of the event, q, approaches 1. This makes the binomial distribution skewed towards 0 and more and more concentrated around the mean.
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In Binomial Distribution if n is infinitely large, the probability p of occurrence of event is close to _______ and q is close to _________a)0 , 1b)1 , 0c)1 , 1d)noneCorrect answer is option 'A'. Can you explain this answer?
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