Question

Medians of binomial and poisson distribution

Answer 1

☆ranshsangwan☆☆


Let

X

X

be a random variable that follows a Poisson distribution with parameter

λ=5

λ=5

, then we have

P(X≤4)≈0.440493

P(X≤4)≈0.440493

and

P(X≤5)≈0.615961

P(X≤5)≈0.615961

. So, it's clearly the median

(

x

50

)

(x50)

of

X

X

is between

4

4

and

5

5

, more precisely

x

50

≈4.32937026824559119408

x50≈4.32937026824559119408

obtained by a computer program. Unfortunately, we are only allowed to use a simple scientific calculator so basically it's difficult to obtain that precise value using a simple scientific calculator by trial and error or Newton method due to time limit. I managed to obtain

x

50

≈4.33

x50≈4.33

by trial and error method, so I answered

4

4

because I rounded to the nearest integer. But some of friends argued and they answered

5

5

because they used the nearest rank method,

x

50

=⌈4.33⌉=5

x50=⌈4.33⌉=5