List of top Questions asked in IIT JAM MS- 2026

Let \(X_1,X_2,X_3\) be a random sample of size \(3\) from \(Exp(1)\) distribution. Then, \(E\left(4X_{(2)}e^{X_{(2)}}\right)\) equals (in integer).

The observed value of a random sample of size \(9\) from a distribution having continuous and strictly increasing cumulative distribution function is as below:

Let \(X_1,X_2,\ldots\) be a sequence of independent and identically distributed random variables with mean \(4\) and variance \(9\). If \(T_n=\frac{1}{n}\sum_{i=1}^{n}X_i\), then

Let \(X_1,X_2\) be a random sample of size \(2\) from a distribution with the probability density function

Let \(X_1,X_2,\ldots,X_n\) be a random sample of size \(n\;(n>1)\) from a \(N(\mu,1)\) distribution, where \(\mu\in\mathbb{R}\) is an unknown parameter. If \(\overline{X}=\frac{1}{n}\sum_{i=1}^{n}X_i\), then the minimum value of \(n\) such that

A fair six-sided die is rolled \(4\) times independently. If \(p\) is the probability that the sum of the outcomes is \(14\), then \(10p\) equals (rounded off to three decimal places).

Consider the real matrices

If \((X,Y)\) is a random vector with the joint probability mass function

Let \(X\) be a random variable with the probability density function

Let \(X_1,X_2,X_3\) be a random sample of size \(3\) from \(U(1,2)\) distribution. Then \(P(X_{(3)}>1.5)\) equals (rounded off to two decimal places).

The area of the region in the first quadrant that is bounded by the parabola

Let \(\{X_n\}_{n\geq 1}\) be a sequence of independent and identically distributed random variables having \(U(0,3)\) distribution. If \(Y_n=\frac{1}{n}\sum_{i=1}^{n}X_i^2,\; n\geq 1\), then \(\{Y_n\}_{n\geq 1}\) converges in probability to (in integer).

Let \(X\) be a continuous random variable with mean \(2\) and variance \(4\). Using Chebyshev's inequality, the lower bound for \(P(-4\leq X\leq 8)\) equals (rounded off to two decimal places).

Let \((X,Y)\) be a random vector having the bivariate normal distribution with \(E(X)=2\), \(E(Y)=10\), \(Var(X)=9\), \(Var(Y)=25\), and the correlation coefficient between \(X\) and \(Y\) equals \(\rho>0\). If

A point is chosen at random from a square region whose sides are of \(2\) metres. If the centre of the square is defined to be the point of intersection of its two diagonals, then the probability that the randomly chosen point is closer to the centre of the square than to any of its four corners equals (rounded off to two decimal places).

Let \(\{N(t),t\geq 0\}\) be a Poisson process with rate \(\lambda=1\). Then \(E[N(8)N(5)]\) equals (in integer).

Let \(X_1,X_2,X_3,X_4\) be a random sample of size \(4\) from a distribution with the probability density function

Let \(f:\mathbb{R}\to\mathbb{R}\) be the function defined by \(f(x)=3e^x\cos 2x\). If \(p(x)=ax^3+bx^2+cx+d\) is the third degree Taylor polynomial of \(f\) at \(x=0\), then \(|a|+|b|+|c|+|d|\) equals (in integer).

In a singing competition, two judges award ranks for each of the \(10\) contestants. Based on the ranks awarded by the two judges, the Spearman’s rank correlation coefficient \(\rho\) for the \(10\) contestants was computed to be \(0.6\). It was found later that the difference in ranks awarded by the two judges for one of the contestants was incorrectly taken as \(2\), instead of the correct value \(5\). If the correct difference is taken into account, then the corrected value of \(\rho\) equals (rounded off to two decimal places).

Let \(Y_1,Y_2\) be a random sample of size \(2\) from a distribution with the probability mass function

Let \(X_1,X_2,\ldots,X_n\) be a random sample of size \(n\;(n>1)\) from an \(Exp(\beta)\) distribution, where \(\beta>0\). If \(T=\sum_{i=1}^{n}X_i\), then which of the following statements is/are true?

If the system of linear equations

Let \(X\) be a random variable with the probability density function

Let \((X,Y)\) be a random vector with the joint probability density function

Consider a simple linear regression model