SSC CGL 2024 (Tier-II) Paper 2 Previous Year Paper (19-Jan-2025)

Question 1

For the bivariate random variable (X,Y), let the joint probability density function be $ f(x, y) = \frac{9(1 + x + y)}{2(1 + x)^4(1 + y)^5} $ for $ 0 < x < \infty, 0 < y < \infty $. The marginal pdf of X is:

Accepted Answer

$\frac{3(2x+3)}{4(1+x)^4}$

Answer

$\frac{3(2x+3)}{2(1+x)}$

Answer

$\frac{3(2x+1)}{4(1+x)^4}$

Answer

$\frac{3(2x+3)}{(1+x)^4}$

Question 2

Monthly sales data (in units) shows the following trend-adjusted ratios for three months: January (1.1), February (0.9), and March (1.0). What is the average seasonal index for this quarter?

Accepted Answer

1.0

Answer

0.95

Answer

0.9

Answer

1.1

Question 3

Duncan’s Multiple Range Test makes use of which statistical measure?

Accepted Answer

Range Statistic (R)

Answer

Standard Error of the Means

Answer

Regression Coefficient

Answer

F-statistic

Question 4

For three random variables $ X_1, X_2 $ and $ X_3 $, the correlation coefficients between pairs of random variables are: $ r_{12} = r_{13} = r_{23} = r \neq 1 $ For $ R_{1,23} $ (multiple correlation coefficient), $ 1 - R_{1,23}^2 $ is written as:

Accepted Answer

$\displaystyle\frac{(1-r)(1+2r)}{1+r}$

Answer

$\displaystyle\frac{(1+r)(1+2r)}{1-r}$

Answer

$\displaystyle\frac{(1+2r)}{1+r}$

Answer

$\displaystyle\frac{(1+r)(1-2r)}{1+r}$

Question 5

What is the primary challenge in using the free-hand curve method for trend estimation?

Accepted Answer

It is subjective and may lead to inconsistent results.

Answer

It is time-consuming and computationally intensive.

Answer

It cannot identify cyclical patterns.

Answer

It requires advanced statistical knowledge.

SSC CGL 2024 (Tier-II) Paper 2 Previous Year Paper (19-Jan-2025)

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