Question

Kindly help with probability based on integrals.
Photo is attached. I am kind of confused as to part a and b. For part a, I've set my lower limit to 1 and upper limit to infinity but the result is ~20 which exceeds 1.

Answer 1

For a)
$$
\text{f(x)=0},\text{for }1<X\le4
$$
Do you see that?

Answer 2

yes, are you not taking zero into consideration or it does not really have an effect?

Answer 3

1 < X is the same as X >1, so zero is not part of the question for this part

Answer 4

Do you see that?

Answer 5

i see that

Answer 6

So any X < 4 is zero, so we should focus only on those values of X > 4. Any X < 4 is zero

Answer 7

I should say, for any x < 4, f(x) = 0

Answer 8

that's much better.

Answer 9

We are given that for X>4
$$
f(x)=e^{-(x-4)}
$$
Which means that for X > 1 (which is what a) is asking us), we only care about X > 4, since
$$
\text{f(x)=0},\text{for }1<X\le4
$$

Answer 10

therefore my limit goes from 4 to infinity.

Answer 11

yes!!

Answer 12

turn gives me a probability of 1. this will be true since 1 is less than x.

Answer 13

yes, this is a pdf, integrating across its entire domain, so the integral will equal to 1

Answer 14

then for part b i just go from 4 to 5.

Answer 15

perfect!

Answer 16

thanks, i needed the understanding. crunching numbers is easy.

Answer 17

You're welcome