List of top Atmospheric Science Questions on Statistics asked in CUET (PG)

The Fourier series expansion is given as: 
\[ \frac{a_{0}}{2} + a_{1}\cos x + a_{2}\cos 2x + \cdots + b_{1}\sin x + b_{2}\sin 2x + \cdots \] 

For the function \[ f(x) = x + \frac{x^{2}}{4}, \quad -\pi \le x \le \pi \] 
The value of \(a_0\) and \(b_2\) are:

Consider the function $f(x)$ for an interval $(-\pi,\pi)$ then which one of the following is NOT correct Dirichlet's condition for a Fourier series?
The determinant of the matrix $\begin{bmatrix}3 & -1& -2\\0& 0& -1\\3 & -5& 0\end{bmatrix}$ is:
The integrating factor of following differential equation is : $\frac{dy}{dx}-\frac{3x^{2}-1}{x^{3}-x}y=x^{2}-1$}
Let $y=A~cos(x)+B~sin(x)$ the differential equation by eliminating A and B constants is given by:
For two correlated data series X and Y, which formula for \( \text{Var}(X-Y) \) is correct?

Identify the median class for the following grouped data:

\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]
 

The arithmetic mean of 10 items is 5. If 5 is added to each of the first seven items and 3 is subtracted from each of the last three items, then the mean of the new data series is:

The coefficient of correlation of the above two data series will be equal to \(\underline{\hspace{1cm}}\)

\[\begin{array}{|c|c|} \hline X & Y \\ \hline -3 & 9 \\ -2 & 4 \\ -1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ 3 & 9 \\ \hline \end{array}\]
 

While writing a computer programming code, it was found that Team A incurred 250 errors in a code of 1000 lines while Team B incurred 300 errors in a code of 800 lines. In order to determine whether Team A has performed better than Team B, a statistical hypothesis was set and tested. Then the value of the test statistic is: