Suppose thatX1, . . . , X11is a random sample from an unknown continuous distribu- tion. (a) By using the binomial distribution withn= 11 andp= 0.5, find a 90% confidence interval for the median of...

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Suppose thatX1, . . . , X11is a random sample from an unknown continuous distribu- tion. (a) By using the binomial distribution withn= 11 andp= 0.5, find a 90% confidence interval for the median of the unknown distribution. That is, find integersr



Answered Same DayDec 25, 2021

Answer To: Suppose thatX1, . . . , X11is a random sample from an unknown continuous distribu- tion. (a) By...

David answered on Dec 25 2021
116 Votes
Median of a binomial distribution:
Let X be a random variable with n =11 and p =0.5
We have pdf of X
P(X=r) = 11Cr(0.5)
r
(0.5)
11-r
= 11Cr(0.5)
11
, r = 0,2,….11
CDF is P(X<=x) = ∑ ( )
For median m, we have P(X<=m) = 0.5
i.e. ∑ ( ) = 0.5
Solving we get...
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