# continuous random variable

• November 4th 2010, 07:40 PM
DINOCALC09
continuous random variable
Please let me know of any errors/wrong logic

f(x) = { |x| for -1 < x <=1 , 0 elsewhere

A) Determine Cumulative Distributin Function...

F(x) = { 0 for x < -1 , -0.5(x^2) for -1 <= x < 0 , 0.5(x^2) for 0 <= x <= 1, 1 for x >1

B) F(-0.25)

(-0.5)(-0.25)^2 = -0.03125

I thought that it should yield a positive value...

C) Pr(-0.25 <= X <= 0.5)

F(B) - F(A) = F(0.5) - F(-0.25) = (0.5)(0.5)^2 - (-0.5)(-0.25)^2 = 0.4375
• November 4th 2010, 08:33 PM
mr fantastic
Quote:

Originally Posted by DINOCALC09
Please let me know of any errors/wrong logic

f(x) = { |x| for -1 < x <=1 , 0 elsewhere

A) Determine Cumulative Distributin Function...

F(x) = { 0 for x < -1 , -0.5(x^2) for -1 <= x < 0 , 0.5(x^2) for 0 <= x <= 1, 1 for x >1 Mr F says: There are multiple obvious errors with this answer. According to this:

1. F(0) = 0 ....? Surely F(0) = 0.5.

2. F(x) < 0 for $-1 \leq x < 0$ which is obviously wrong.

3. F(1) = 0.5 and so your cdf is not continuous.

B) F(-0.25)

(-0.5)(-0.25)^2 = -0.03125

I thought that it should yield a positive value...

C) Pr(-0.25 <= X <= 0.5)

F(B) - F(A) = F(0.5) - F(-0.25) = (0.5)(0.5)^2 - (-0.5)(-0.25)^2 = 0.4375

You need to fix up your answer to part (a) before worrying about the other parts. I hope you know that |x| = -x for x < 0 and so for x < 0, $F(x) = \int_{-1}^x (-u) \, du$ ....
• November 5th 2010, 10:09 AM
DINOCALC09
Ok so I think I figured it out:

F(x) =

0 for x< -1
(1-x^2)/2 for -1 <= x <= 0
(1+x^2)/2 for 0 < x <= 1
1 for x > 1

Now how would I go about finding the IQR here?

Thanks
• November 5th 2010, 01:57 PM
mr fantastic
Quote:

Originally Posted by DINOCALC09
Ok so I think I figured it out:

F(x) =

0 for x< -1
(1-x^2)/2 for -1 <= x <= 0
(1+x^2)/2 for 0 < x <= 1
1 for x > 1

Now how would I go about finding the IQR here?

Thanks

Get the 25th and 75th percentiles and then take the difference of them.