**1. The problem statement, all variables and given/known data**

Consider a sample of size 5 from a uniform random distribution (0,1) . Computer the probability that the median is in the interval (1/4, 3/4).

Consider a sample of size 5 from a uniform random distribution (0,1) . Computer the probability that the median is in the interval (1/4, 3/4).

**2. Relevant equations**

I guess....

The Pdf of beta is

and median is....I'm not sure....I would guess 1/2?

I guess....

The Pdf of beta is

and median is....I'm not sure....I would guess 1/2?

**3. The attempt at a solution**

okay, so I'm not even sure where to begin with this. It looks as though they are giving me a uniform problem but in a two dimensional space. Then i remembered, okay the chapter I'm dealing with is Jointly Distributed Random variables. Median is 1/2 (a + b), so 1/2.

The answer in the back of my book says that it is exactly .79297

Okay so i get that P{1/4 <x<3/4} and since sample is 5 I have to multiply that by what i get when I Integrate the density so 5 Int(x)

but I'm using one of the old ross books and I believe it said, I'm supposed to use the formula x(1-x) but I tried that and got total np= .5078. tried the regular way and it exceeded one...

eventually figured out it's a beta distribution, and that there wasn't some weird thing I was missing in uniform. But I have no clue how to go about a is 1/4 and b is 3/4

how do I arrange the pdf of this?

okay, so I'm not even sure where to begin with this. It looks as though they are giving me a uniform problem but in a two dimensional space. Then i remembered, okay the chapter I'm dealing with is Jointly Distributed Random variables. Median is 1/2 (a + b), so 1/2.

The answer in the back of my book says that it is exactly .79297

Okay so i get that P{1/4 <x<3/4} and since sample is 5 I have to multiply that by what i get when I Integrate the density so 5 Int(x)

but I'm using one of the old ross books and I believe it said, I'm supposed to use the formula x(1-x) but I tried that and got total np= .5078. tried the regular way and it exceeded one...

eventually figured out it's a beta distribution, and that there wasn't some weird thing I was missing in uniform. But I have no clue how to go about a is 1/4 and b is 3/4

how do I arrange the pdf of this?