f(x)= 2(x-1)/3 in the interval 1<x<2 and 4-x/3 in the intervals 2<x<4 and 0 otherwise there are 3 f(x) and I am familiar with finding the unknown variable k when there is one f(x) but in this problem there is 2 main ones the 0 is useless but I don't know which equation to fill in the numbers I tries both but they were wrong the answers spouse to be 2 but I don't know how to get it . Any help is really appreciated! This is in the topic continuous random variables in statistics and probbaility.
So if you check this $f$ given would be a density function for a random variable $X$ What this would mean $$\int_1^4 f(x)dx = 1$$ So what you want is to find a $k$ s.t. $$\int_1^k f(x)dx \le 1/3$$ Now the form of $f$ is given. So if $f$ was defined in the same way over the entire domain then you could replace $f$ with that definition and performed an integration with $k$ being solved as an unknown. However as $f$ is defined over 2 intervals you should take care and take 2 cases. One when $k$ belongs to the first and the other when $k$ belongs to the second and proceed in the manner similar to if there was only a single equation. Ofcourse since $f$ is a density function the value of $k$ would be unique. So you have to eliminate one of the choices of $k$ you get from considering the 2 equations using the definition of the function.