Advertisements
Advertisements
Question
Write the conditions for which the poisson distribution is a limiting case of binomial distribution
Advertisements
Solution
Poisson distribution is a limiting case of binomial distribution under the following conditions:
(i) n, the number of trials is indefinitely large i.e n → `∞`
(ii) p, the constant probability of success in each trial is very small, i.e. p → 0.
(iii) np = λ is finite.
Thus p = `lambda/"n"` and q = `1 - (lambda/"n")`
Where λ, is a positive real number.
APPEARS IN
RELATED QUESTIONS
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?
Out of 750 families with 4 children each, how many families would be expected to have atleast one boy
Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be no phone at all
Write down any five chief characteristics of Normal probability curve
Choose the correct alternative:
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
Choose the correct alternative:
In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
