List of top Mathematics Questions asked in GATE Electrical Engineering

Let \( X \) and \( Y \) be continuous random variables with probability density functions \( P_X(x) \) and \( P_Y(y) \), respectively. Further, let \( Y = X^2 \) and \[ P_X(x) = \begin{cases} 1, & x \in (0,1] \\ 0, & \text{otherwise} \end{cases} \] Which one of the following options is correct?

Consider discrete random variables \( X \) and \( Y \) with probabilities as follows:

\( P(X=0 \text{ and } Y=0) = \frac{1}{4}, \)
\( P(X=1 \text{ and } Y=0) = \frac{1}{8}, \)
\( P(X=0 \text{ and } Y=1) = \frac{1}{2}, \)
\( P(X=1 \text{ and } Y=1) = \frac{1}{8}. \)

Given \( X = 1 \), the expected value of \( Y \) is

Consider the set \( S \) of points \( (x, y) \in \mathbb{R}^2 \) which minimize the real-valued function \( f(x, y) = (x + y - 1)^2 + (x + y)^2 \). Which of the following statements is true about the set \( S \)?

For a given vector \( \mathbf{w} = [1 \; 2 \; 3]^T \), the vector normal to the plane defined by \( \mathbf{w}^T \mathbf{x} = 1 \) is:

Which one of the following options represents the given graph? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}