GATE 2017 CS (CS2) – Question 58

Engineering Mathematics · Probability and Statistics · 2 marks · Numerical answer

X is Poisson with mean 5. Find E[(X+2)²].

Show answer and explanation

Correct answer: 54.0 to 54.0

Explanation

For Poisson X, E[X]=Var(X)=5. Therefore E[X²]=Var(X)+(E[X])²=5+25=30. Expanding gives E[(X+2)²]=E[X²]+4E[X]+4=30+20+4=54.

GATE 2012 CS (CS1) Q31 – X equals −1 or +1 with probability 0.5 each. Find F(−1),F(+1) for its cumulative…
GATE 2012 CS (CS1) Q43 – Roll a fair six-sided die once. If the first value is 1,2 or 3, roll again. What is the…
GATE 2013 CS (CS1) Q12 – Cars per minute at a junction between 5 PM and 6 PM follow a Poisson distribution with…
GATE 2013 CS (CS1) Q34 – An undirected random graph has eight vertices, each possible edge independently present…
GATE 2011 CS (CS1) Q13 – Two fair coins are flipped. At least one outcome is known to be a head. What is the…
GATE 2011 CS (CS1) Q28 – Let R=E[X2]-(E[X])2. Which always holds?