Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y = X1 - X2; μ1 = μ2 = 1, σ1 = 1, σ2 = 2, Then,

Y is normally distributed with mean 0 and variance 5

Y is normal distributed with mean 0 and variance 1

Y is normally distributed with mean 0 and variance 5

Y has mean 0 and variance 5, but is NOT normally distributed

Y has mean 0 and variance 1, but is NOT normally distributed

Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y = X1 - X2; μ1 = μ2 = 1, σ1 = 1, σ2 = 2, Then,

Which two of the following statements are true? a) The sum of the deviations from mean (ignoring algebraic signs) is greater than the sum of the deviations from median (ignoring algebraic signs) b) Standard deviation is independent of change of origin and change of scale c) In a symmetrical distribution, mean deviation equals 4/5 of standard deviation d) In a symmetrical and bell shaped distribution quartile deviation is 1/3 of standard deviation Choose the correct answer from the options given below

A

b) and d)

B

a) and c)

C

c) and d)

D

a) and b)

Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:

A

1, 2 and 3

B

1, 3 and 4

C

Both 2 and 4

D

2, 3 and 4

A company recruits candidates satisfying the following criteria - 1. Candidates who secured at least 85% in standard 10th or equivalent. 2. Candidates who secured at least 65% in standard 12th or equivalent. 3. Candidates who are not from commerce background. Who among the following candidates will the company definitely select? A. Jitesh is a science student having scored 70% in standard 12th and 80% in 10th with an excellent sports background. B. Jignesh scored 80% in standard 12th, 90% in standard 10th and secured 2nd place in his college among all commerce students. C. Jayesh scored 75% in standard 10th, 75% in standard 12th and is an arts student. D. Jinesh secured 80% in standard 12th, 88% in standard 10th and is a science student with great acting skills

A

B

D

C

D

A

What is linear_congruential_engine? for some w using Mersenne Twister algorithm b) Pseudo-random number engine that generates random unsigned integers c) Pseudo-random number engine that generates random unsigned integers in the range for some w using lagged Fibonacci generator d) Pseudo-random number engine that generates random signed integers in the range for some w using Mersenne Twister algorithm

A

Pseudo-random number engine that generates random unsigned integers in the range for some w using Mersenne Twister algorithm

B

0, 2w-1

C

0, 2w-1

D

0, 2w-1

The given table shows the number of students and their class. Division A students are scholars who get a 25% rebate in fees. In addition, all girls students get 40% subsidy. If the fee per student a year WITHOUT rebate or subsidy is Rs. 10,000, then find the total fees collected from the students of these 6 classes for that year. Division /Standard Boys Girls Division A /Standard 9 20 40 Division B /Standard 9 40 35 Division C /Standard 10 20 20 Division A /Standard 10 40 20 Division B /Standard 10 20 40 Division C /Standard 10 20 15

A

Rs. 23.2 lakh

B

Rs. 22.6 lakh

C

Rs. 21.4 lakh

D

Rs. 20.2 lakh

Let X₁ and X₂ be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X₁, X₂) is

A

exponentially distributed with mean $$\frac{1}{6}$$

B

exponentially distributed with mean 2

C

normally distributed with mean $$\frac{3}{4}$$

D

normally distributed with mean $$\frac{1}{6}$$

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2) the standard deviation of Y is

A

3

B

2

C

√2

D

1

Refer the below data table and answer the following Question : Division/Standard Boys Girls Division A/Standard 5 20 30 Division B/Standard 5 15 20 Division C/Standard 5 30 10 Division A/Standard 6 30 25 Division B/Standard 6 30 25 Division C/Standard 6 30 20 What is the ratio of Boy’s to Girl’s?

A

26 : 31

B

31 : 26

C

33 : 28

D

28 : 33

Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.

A

Both statements are correct

B

Both statements are incorrect

C

Statement I is correct while Statement II is incorrect

D

Statement I is incorrect while Statement II is correct

Assertion (A): When there is an evidence of a linear relationship between two variables, it may not always mean an independent-dependent relationship between the two variables.
Reason (R): The casual relationship between the two variables may not imply a reasonable theoretical relationship between the two.

A

Both (A) and (R) are true and (R) is the correct explanation of (A)

B

Both (A) and (R) are true, but (R) is not the correct explanation of (A)

C

(A) is true, but (R) is false

D

(A) is false, but (R) is true

Let X₁, X₂ be two independent normal random variables with means μ₁, μ₂ and standard deviations σ₁, σ₂ respectively. Consider Y = X₁ - X₂; μ₁ = μ₂ = 1, σ₁ = 1, σ₂ = 2, Then,

Related Questions