continuous distribution

• Sep 27th 2006, 04:11 AM
scorpion007
continuous distribution
X is a random variable with probability density function defined as:

f(x) = {
2sin(4x), a <= x <= b
0, elsewhere
}

find a and b?
• Sep 27th 2006, 06:12 AM
Plato
You know that the value your function must be non-negative.
The total area under the curve must be 1.
Therefore, let a=0 and find b.
• Sep 27th 2006, 06:24 PM
scorpion007
hmm, if i let a=0, i get the wrong answer straight away.

The book says: PI/2, 3*PI/4 for a and b respectively.

I tried solving the question and i got 0 <= x <= PI/4 -- which seems to be also correct, as the answer they give is basically exactly 1 period later.
Since 0 + PI/2 = PI/2, and PI/4 + PI/2 = 3*PI/4

So i think i basically got it right, just that my answer wasnt any of the multiple choices.

Btw, the way i solved it (which is basically what you said) was:

2sin(4x) >= 0
sin(4x) >= 0
4x >= asin(0)
4x >= 0, PI
x >= 0, PI/4

so 0 <= x <= PI/4

and i checked the integral from 0 - PI/4 of 2sin4x to make sure it == 1.