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

Question

anonymous · Answer

f(x) = {0.075x + 0.2   3≤x≤5
          {     0                otherwise

Calculate P(X≤4). How does this probability compare to P(X<4)?

I calculated (0.075x + 0.2)dx on the interval of 3 to 4. The answer in the back of the book was 0.25, but is this really correct?

loser66 · Answer

I don't know. To me, $P(x\leq 4)$ is the same as $P(x<4)$
And my answer is 0.4625, not 0.25 :(

loser66 · Answer

@Zarkon

anonymous · Answer

Yeah, that's the same answer I got. Hrm...

kropot72 · Answer

My result is the same:$$\large P(X \le4)=0.4625$$

zarkon · Answer

For any continuous rv $X$ we have $P(X=a)=0$ for any constant $a$


therefore 

$$P(X\le 4)=P(X<4 \text{ or } X=4)$$
$$=P(X<4)+P(X=4)=P(X<4)+0=P(X<4)$$

loser66 · Answer

Yes, now it is clear for why $P(x\leq 4)$ is same as $P(x< 4)$. How about the answer?  How can they get 0.25?

zarkon · Answer

it is a mistake

zarkon · Answer

either RightInTheCranium looked at the wrong answer or the answer in the book is not correct  (or the problem was typed wrong)

loser66 · Answer

Yeaaaaaaaah!! If it is not, I do not want to study statistics any more. :)

loser66 · Answer

Thanks a lot @Zarkon

anonymous · Answer

Double and triple checked. Back of the book says 0.5. 

Thanks for the help though! Glad to know I'm not just spinning my wheels.