The current in a certain circuit as measured by an ammeter is
a continuous random variable X with the following density
function:

f(x) = {.75x + .2 | 3=

Question

The current in a certain circuit as measured by an ammeter is
a continuous random variable X with the following density
function:

f(x) = {.75x + .2 | 3=<X=<5

eujc21 · Answer

attachment

anonymous · Answer

Graph the pdf: Just graph it.
$$P(x \le4)=\int\limits_{3}^{4}f(x)dx ;  P(x \le4) = P(x<4)$$ because this a continuous distr.  The probability at a single point is 0.  Why?  The area under a single point is 0.
$$P(3.5 \le x \le 4.5) = \int\limits_{3.5}^{4.5}f(x)dx$$
$$P(X>4.5)=P(4.5 < x < 5) = \int\limits_{4.5}^{5}f(x)dx$$