Hindi
English

Question

Download Solution PDF

यदि एक सतत यादृच्छिक चर x का प्रायिकता घनत्व फलन 

है, तो a का मान इस प्रकार क्या होगा कि P[x ≤ a] = P[x > a] है?

This question was previously asked in
SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )
Download PDF Attempt in App
View all SSC CGL Papers >
  1. 1 / 2
  2. 1 / 3

Answer (Detailed Solution Below)

Option 4 :
super-subscription-prototype
Free Tests
View all Free tests >
Free
PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
25 Qs. 50 Marks 12 Mins
Start Now

Detailed Solution

Download Solution PDF

दिया गया है

गणना 

P(X < a) = 1/a2 = 

⇒ x2dx = 1/2

⇒ 3[x3/3]a0 = 1/2

⇒ 3 × (a3/3 - 0) = 1/2

⇒ a3 = 1/2

∴ a का मान इस प्रकार कि P[x ≤ a] = P[x > a], (1/2)1/3 है। 

Download Solution PDF
Latest SSC CGL Updates

Last updated on Jun 13, 2025

-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.

-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

->  The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> Candidates should also use the SSC CGL previous year papers for a good revision. 

Exams Tests Super Practice

More Random Variables Basics Questions

Q1.एक अनभिनत सिक्के को 5 बार उछाला जाता है। मान लीजिए कि चर \(X\) को \(k = 3, 4, 5\) के लिए लगातार \(k\) चित प्राप्त होने पर मान \(k\) दिया जाता है, अन्यथा \(𝑋\) का मान \(-1\) होता है। \(X\) का अपेक्षित मान है:
Q2.A man draws 3 balls from a jug containing 5 white balls and 7 black balls. He gets Rs. 20 for each white ball and Rs. 10 for each black ball. What is his expectation?
Q3.यदि एक यादृच्छिक चर X का घनत्व फलन f(x) = \(\left\{\begin{array}{l}\frac{1}{2},−1<x<1\\ 0. \text { otherwise }\end{array}\right.\) है तो P(|X|>1) है:
Q4.A random variable y has a known probability distribution given by y 2 4 6 8 10 P(y) 0.17 0.23 0.2 0.3 0.1 Then the expected value of y is
Q5.Let the probability density function of a random variable x be given as f(x) = ae-2|x| The value of ‘a’ is __________. 
Q6.यदि एक यादृच्छिक चर X का प्रत्याशित मान 2 है और उसका प्रसरण 1 है, तो 3X + 4 का प्रसरण क्या होगा?
Q7.यदि x प्रायिकता घनत्व फलन के साथ एक सतत यादृच्छिक चर है f(x) = 1/√2πe-x2/2dx , \( - ∞<x<∞\) और y को y = x + 1 के रूप में परिभाषित किया गया है, तो E(y) किसके बराबर है?
Q8.x और y का संयुक्त बंटन इस प्रकार है x→ 1 2 y↓     1 0.4 0.2 2 0.1 0.3 तो E(x|y = 1)                           है। 
Q9.मान लीजिए x ~ द्विपद (5,0.6) और Y ~ पॉइसन (2) स्वतंत्र हैं। तो P(xy = 0) किसके बराबर है?
Q10.यदि एक सतत यादृच्छिक चर x का प्रायिकता घनत्व फलन  \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {3x^2,}&o\le x\le1\\ {0,}&{elsewhere} \end{array}} \right.\) है, तो a का मान इस प्रकार क्या होगा कि P[x ≤ a] = P[x > a] है?

More Probability and Statistics Questions

Q1.एक अनभिनत सिक्के को 5 बार उछाला जाता है। मान लीजिए कि चर \(X\) को \(k = 3, 4, 5\) के लिए लगातार \(k\) चित प्राप्त होने पर मान \(k\) दिया जाता है, अन्यथा \(𝑋\) का मान \(-1\) होता है। \(X\) का अपेक्षित मान है:
Q2.एक बैग में 7 सफेद, 6 लाल और 9 काली गेंदें हैं। दो गेंदों को यादृच्छिक रूप से निकाला जाता है, तो निकाली गई गेंद के काले होने की प्रायिकता क्या होगी?
Q3.सूत्र \(\rm \overline X=A+\frac{\Sigma fiμ i}{\Sigma f}\times h\) में , μi = ?
Q4.A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest? 
Q5.Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?
Q6.Dimension reduction methods have the goal of using the correlation structure among the predictor variables to accomplish which of the following: A. To reduce the number of predictor components B. To help ensure that these components are dependent C. To provide a framework for interpretability of the results D. To help ensure that these components are independent E. To increase the number of predictor components Choose the correct answer from the options given below: 
Q7.A man draws 3 balls from a jug containing 5 white balls and 7 black balls. He gets Rs. 20 for each white ball and Rs. 10 for each black ball. What is his expectation?
Q8.यदि वास्तविक रेखा पर f(x) कोई प्रायिकता घनत्व है तो निम्न में से कौन-सा वैध प्रायिकता घनत्व नहीं है?
Q9.Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If the securities with less than perfect negative correlation between their price movements are combined, portfolio risk can be reduced significantly. Reason (R): The term with negative correlation has the effect of reducing the computed value of total portfolio risk, given other terms that are positive. In the light of the above statements, choose the most appropriate answer from the options given below:
Q10.A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on even- and odd-numbered dates, respectively. If 100 vehicles are chosen at random on an even-numbered date, the number of vehicles expected without pollution clearance certificate is ________.
Suggested Test Series
View All >
SSC CGL (Tier I & Tier II) Mock Test 2025 (New)
1113 Total Tests with 4 Free Tests
Start Free Test
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with   4 Free Tests
Start Free Test

SSC CGL Important Links

SSC CGL SyllabusRank PredictorAdmit CardCut OffPrevious Year PapersExam Dates

More Engineering Mathematics Questions

Q1.यदि L = {1, 2, 3, 4, 6, 9, 36} जालक है, तो नीचे दिए गए हैस आरेख में 9 के पूरकों की संख्या ज्ञात कीजिए।
Q2.अनिर्देशित आलेख के लिए निम्नलिखित में से कौन सा/से कथन सत्य है?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： happy teen patti teen patti comfun card online teen patti master list teen patti cash game dhani teen patti