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 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are find the mean and variance
In a family of 3 children, what is the probability that there will be exactly 2 girls?
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15)
It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute no customer appears
X is normally distributed with mean 12 and SD 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)
Choose the correct alternative:
Normal distribution was invented by
Choose the correct alternative:
The time until the first failure of a brand of inkjet printers is normally distributed with a mean of 1,500 hours and a standard deviation of 200 hours. What proportion of printers fails before 1000 hours?
