Question
Download Solution PDFIn a Binomial Distribution (BD) the mean is 15 and variance is 10, then parameter n (number of trials) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Binomial distribution: If a random variable X has binomial distribution as B (n, p) with n and p as parameters, then the probability of random variable is given as:
P( X = k) = nCk pk (1 - p)(n - k)
Where, n is number of observations, p is the probability of success & (1 - p) is probability of failure.
Properties:
- Mean of the distribution (μX) = n × p
- The variance (σ2x) = n × p × (1 - p)
- Standard deviation (σx) =
Calculation:
Given:
mean of BD = np = 15
And variance of BD = npq = 10
⇒ np(1 – p) = 10 (∵ p + q = 1)
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.