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Recent questions tagged isi2015
13
votes
2
answers
1
ISI2015-MMA-7
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }-1}{\lambda }$ $\frac{e^{\lambda }-1}{\lambda +1}$ $\frac{1-e^{-\lambda }}{\lambda}$ $\frac{1-e^{-\lambda }}{\lambda + 1}$
neha.i
asked
in
Probability
May 11, 2017
by
neha.i
2.0k
views
isi2015
engineering-mathematics
poisson-distribution
11
votes
1
answer
2
ISI 2015 PCB C4 A
Design a context free grammar for the language consisting of all strings over $\mathbf{\{a,b\}}$ that are not the form $\mathbf{ww}$ for any string $\mathbf{w}$
Devasish Ghosh
asked
in
Theory of Computation
Mar 9, 2017
by
Devasish Ghosh
1.0k
views
pushdown-automata
theory-of-computation
isi2015
12
votes
2
answers
3
ISI 2015 PCB C2 B
You are given a array $A$ of size $n$. Your are told that $A$ comprises three consecutive runs - first a run of $a$'s, then a run of $b$'s and finally a run of $c$'s. Moreover, you are provided an index of $i$ such that $A[i] = b$. Design an $O(\log n)$ time algorithm to determine the number of $b$'s (i.e., length of the second run) in $A$.
Devasish Ghosh
asked
in
DS
Mar 8, 2017
by
Devasish Ghosh
1.3k
views
data-structures
array
isi2015
11
votes
2
answers
4
ISI2015-PCB-C3
For a positive integer $n$, let $G = (V, E)$ be a graph, where $V = \text{{0,1}}^n$, i.e., $V$ is the set of vertices has one to one correspondence with the set of all $n$-bit binary strings and $E = \{(u,v) \mid u, v$ belongs to $V, u$ and $v$ differ in exactly one bit position$\}$. Determine size of $E$ Show that $G$ is connected
Devasish Ghosh
asked
in
Graph Theory
Mar 8, 2017
by
Devasish Ghosh
1.1k
views
graph-theory
discrete-mathematics
isi2015
graph-connectivity
3
votes
1
answer
5
ISI 2015 PCB A2
Find all real solutions of the equation $x^{2} - |x-1| - 3 = 0$
Devasish Ghosh
asked
in
Others
Mar 4, 2017
by
Devasish Ghosh
401
views
engineering-mathematics
quadratic-equations
isi2015
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