Question
Download Solution PDFFor the probability distribution given by
X = xi |
0 |
1 |
2 |
pi |
|
|
|
the standard deviation (σ) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For a random variable X = xi with probabilities P(X = xi) = pi:
- Mean/Expected Value: μ = ∑pixi.
- Variance: Var(X) = σ2 = ∑pi(xi)2 - (∑pixi)2 = ∑pi(xi)2 - μ2.
- Standard Deviation: σ =
.
Calculation:
We have x1 = 0, x2 = 1, x3 = 2 and p1 =
∑pixi =
∑pi(xi)2 =
∴ Var(X) = σ2 = ∑pi(xi)2 - (∑pixi)2 =
⇒ Standard Deviation = σ =
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.