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Throw N balls at random into B boxes. Let a be the average number of balls, N/B, in a box. Let P(x) be the probability that a given box has exactly x balls in it. (a) Show that P(x) ≈ a x e −a x! . Certain assumptions are needed for this expression to be valid. What are they? (b) Show that if a is large, the above Poisson distribution essentially becomes a Gaussian distribution, P(x) = a x e −a x! ≈ e −(x−a) 2/2a √ 2πa

Throw N balls at random into B boxes. Let a be the average number of balls, N/B,
in a box. Let P(x) be the probability that a given box has exactly x balls in it.
(a) Show that
P(x) ≈
a
x
e
−a
x!
.
Certain assumptions are needed for this expression to be valid. What are
they?
(b) Show that if a is large, the above Poisson distribution essentially becomes a
Gaussian distribution,
P(x) = a
x
e
−a
x!

e
−(x−a)
2/2a

2πa
 

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Hi student,
The question is not complete and clear
Plsese post it once again

thanks

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