List of top Statistics Questions on Probability asked in IIT JAM MS

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).

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

Let \(S=\{1,2,3,\ldots\}\) and suppose that every subset of \(S\) is an event. Let \(\mathcal{P}(S)\) denote the power set of \(S\). Which of the following statements is/are true?

Consider a discrete time Markov chain with state space \(S=\{1,2,3\}\) and the transition probability matrix

Let \(A,B,C\) be three events such that \(P(C)P(C^c)>0\). Consider the following statements.

Consider a discrete time Markov chain with state space \(S=\{1,2\}\) and the transition probability diagram. If \(\pi=(\pi_1,\pi_2)\) is the stationary distribution of the Markov chain, then which one of the following statements is true?