List of top Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

Let {X_n}_n≥1 be a sequence of independent and identically distributed random variables having U(0, 1) distribution. Let Y_n = n min{X₁, X₂ , … , X_n}, n ≥ 1. If Y_n converges to Y in distribution, then the median of Y equals __________ (round off to 2 decimal places)

\(\lim\limits_{n \rightarrow \infin}\frac{6}{n+2}\left\{(2+\frac{1}{n})^2+(2+\frac{2}{n})^2+...+(2+\frac{n-1}{2})^2\right\}\) equals

Suppose that a fair coin is tossed repeatedly and independently. Let X denote the number of tosses required to obtain for the first time a tail that is immediately preceded by a head. Then E(X) and P(X > 4), respectively, are

Suppose that four persons enter a lift on the ground floor of a building. There are seven floors above the ground floor and each person independently chooses her exit floor as one of these seven floors. If each of them chooses the topmost floor with probability \(\frac{1}{3}\) and each of the remaining floors with an equal probability, then the probability that no two of them exit at the same floor equals

The value of
\(\int^2_0 \int_0^{2-x}(x+y)^2e^{\frac{2y}{x+y}}\ dy\ dx\)
equals __________ (round off to 2 decimal places)