Uniform continuous distribution

[kuba99]

I have those to Problems to solve, can you guys please show me solution ?

 

[Romsek]

1) write out the formula of the PDF, f(x), of this uniform distribution
2) integrate it to obtain the associated CDF, F(x)
3) P[a <= X <= b] = F(b)-F(a)

 

[pka]

I have those to Problems to solve, can you guys please show me solution ?

You really do not need any calculus to work these.
For the first realize that \(\displaystyle (0.5<X<2)\subset [0,8]\) is \(\displaystyle \frac{3}{2} \) of \(\displaystyle 8\).
For the other \(\displaystyle X<6\) is how much of the whole?

 

[kuba99]

Okey, im getting it that we should substract a from b, but should we do something else because i'm guessing that answer is 3/16, but i have no idea where 16 come from, sorry guys for my questions, but i didn't know that on graphic design studies i will learn thing like this...

 

[pka]

Okey, im getting it that we should substract a from b, but should we do something else because i'm guessing that answer is 3/16, but i have no idea where 16 come from, sorry guys for my questions, but i didn't know that on graphic design studies i will learn thing like this...

Can you evaluate this fraction: \(\displaystyle \frac{\frac{3}{2}}{8}~?\)

 

[kuba99]

ok, now i understand, thank you @pka so much ?

 

[kuba99]

@pka im guessing it will be something like this 11'th example

 

[pka]

@pka im guessing it will be something like this 11'th example

I have absolutely no idea what you are asking about.
I am very glad to be of help. BUT I really dislike being thrown into the middle of a question without any way to know what on on.
To get my help in the future, state the complete question say with what you need help.

 

[kuba99]

@pka ok, I will remember, Im asking about 11'th example (Problem 11), I tried to solve it by myself, and if this is no problem can you check if I did it right?
Description for problem 11: Random variable X has uniform continuous distribution on the interval [0, 8].
11. If F is the cummulative distribution function for X, then F(6) = ?
My solution: F(6) = 6/8 = 3/4

 

[Steven G]

This problem is actually simple.
Since it is uniformly continuous you have a rectangle. So please draw one.
The base of the rectangle goes from 0 to 8. So the base has a length of 8.
Now the whole area of the rectangle must equal 1 making the height of the rectangle 1/8. Label the height of the rectangle 1/8.
Now you want to find the area (of a simple rectangle!) from .5 to 2. So the base is just 3/2 and the height is 1/8. The area is 3/2 * 1/8 = 3/16.

F(6) is the cumulative area up to 6. So the base goes from 0 to 6 and the height is 1/8 so F(6) = 6 * 1/8 = 3/4 or just see that the area from 0 to 6 is 3/4 of the entire area and 3/4 of 1 is 3/4

 

[pka]

@pka ok, I will remember, Im asking about 11'th example (Problem 11), I tried to solve it by myself, and if this is no problem can you check if I did it right?
Description for problem 11: Random variable X has uniform continuous distribution on the interval [0, 8].
11. If F is the cummulative distribution function for X, then F(6) = ?
My solution: F(6) = 6/8 = 3/4

\(\displaystyle F(6)=\mathcal{P}(X\le 6)=\frac{6}{8}\) So CORRECT!