English
Hindi

Question

Download Solution PDF

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

  1. E(XY) = E(X) E(Y)
  2. Cov(X, Y) = 0
  3. Var (X + Y) = Var (X) + Var(Y)
  4. E(X2Y2) = (E(X))2 (E(Y))2

Answer (Detailed Solution Below)

Option 4 : E(X2Y2) = (E(X))2 (E(Y))2

Detailed Solution

Download Solution PDF

Explanation:

For X and Y be two independent random variables.

i) E(XY) = E(X) E(Y)

ii) Cov (X,Y) = E (XY) - E(X) E(Y) ⇒ E(X) E(Y) - E(X) E(Y) = 0

iii) Var (X + Y) = Var(X) + Var(Y)

iv) E(X2Y2) = E(X2) E(Y2)

∴ E(X2Y2) = E(X2) ⋅ E(Y2) is the incorrect option

Download Solution PDF
Latest BPSC Assistant Professor Updates

Last updated on Jun 23, 2025

-> The Document Verification for BPSC Assistant Professor (Advt. No. 04/2025 to 28/2025) will be conducted between 7th July 2025 to 24th July 2025

-> The BPSC Assistant Professor Notification 2025 was released for 1711 vacancies under Speciality (Advt. No.04/2025 to 28/2025).

-> The recruitment is ongoing for 220 vacancies (Advt. No. 01/2024 to 17/2024).

-> The salary under BPSC Assistant Professor Recruitment is approximately Rs 15600-39100 as per Pay Matrix Level 11. 

-> The selection is based on the evaluation of academic qualifications &  work experience and interview.

-> Prepare for the exam using the BPSC Assistant Professor Previous Year Papers. For mock tests attempt the BPSC Assistant Professor Test Series.

Exams Tests Super Practice

More Statistical Variables Questions

Q1.In formula \(\rm \overline X=A+\frac{\Sigma fiμ i}{\Sigma f}\times h\), μi = ?
Q2.The mean deviation from the median of the following series is : Serial number 1 2 3 4 5 6 7 8 9 Marks out of 100 68 49 32 21 54 38 59 66 41
Q3.Find the median class of the data whose graph is shown below .
Q4.If the coefficient of variation of two distributions are 30% and 40%, and their arithmetic means are 70 and 60, respectively, then the difference between their standard deviations is:
Q5.The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is __________ (rounded off to one decimal place).
Q6.If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increases by:
Q7.To calculate relative standard deviation
Q8.In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was
Q9.The formula to calculate the coefficient of quartile deviation is
Q10.Sum of mode and median data 12, 15, 11, 13, 18, 11, 13, 12, 13

More Probability and Statistics Questions

Q1.An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise 𝑋 takes the value -1. The expected value of X, is
Q2.A bag contains 7 white, 6 red and 9 black balls. Two balls are drawn at random, the probability that the ball will be black is :
Q3.In formula \(\rm \overline X=A+\frac{\Sigma fiμ i}{\Sigma f}\times h\), 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.If f(x) is a probability density on the real line, then which of the following is NOT a valid probability density?
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 >
71st BPSC CCE (Preliminary) Test Series 2025
222 Total Tests with 1 Free Tests
Start Free Test
BPSC ASO Mock Test Series 2025
143 Total Tests with   4 Free Tests
Start Free Test

BPSC Assistant Professor Important Links

Syllabus & Exam PatternEligibilitySalary and Job ProfileAdmit CardResultsCut off

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
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： teen patti teen patti rummy teen patti casino teen patti sequence