Hint:
If , what are the possible values of X?
Well this is the question in the tutorial:
A random variable X has the density function f(x) = c/(x^2 +1), x is a real number.
a) Find the value of the constant c (already solved) [ans:1/pi]
b) Find the probability that X^2 lies between 1/3 and 1 [ans: 1/6]
well i understand what they want for part (a) which i had already solved but i don't understand part (b) especially on the X^2. Don't really know how it affects the function given for random variable X. Anyone mind explaining?
i just did this:
1/3 < x^2 <1
sqrt(1/3) < x < sqrt(1) and -sqrt(1/3) > x > -sqrt(1)
so this kinda give me two probabilities to solve o.o"
well i solved for the first part and i got 1/12 so since the intervals are of the same range i multiplied the value obtained by 2 to get 1/6 o.o" is
it correct?
Wait, I just have a problem :
So or
This seems strange to me that the bounds are like this, but I can't find the mistake, and this makes me disagree with your probabilities :/
Edit : nevermind... I was just confused >_<
I didn't check the calculus, but it's correct, since the second inequality is the same as the first one (with x instead of -x) and the density function is even