X is a random variable with probability density function defined as:

f(x) = {

2sin(4x), a <= x <= b

0, elsewhere

}

find a and b?

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- Sep 27th 2006, 04:11 AMscorpion007continuous 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 AMPlato
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 PMscorpion007
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.