M (t)= (e^5t- e^4t) / t, t not equal to 0. M(0)= 1. Find P(4.2

Question

M (t)= (e^5t- e^4t) / t, t not equal to 0. M(0)= 1. Find P(4.2< X <= 4.7)

zzr0ck3r · Answer

What is P?

minatsukisaya95 · Answer

probability

zzr0ck3r · Answer

ahh, our of my world, can you tell me how it is defined?

amorfide · Answer

Verify that it is a pdf 
draw the graph, it is never going to go below the axes woo

so now, you want to work out the probability 4.2<X<4.7
M(t) is the height of the curve at X = t
the total area under the curve must be 1 (to be a pdf). In the continuous case, it is areas under the curve that define the probabilities. 
and how do you get the area of a curve? you guessed it! Integration!

So we have
$$\int\limits_{X_{1}}^{X_{2}} M(t) dt$$
I think this is what you are after (I suppose we will know if you get an answer between 0 and 1 lol
but interesting thing to mention, if t can not equal 0 then why does it say M(0)=1, this contradicts itself and says that t can indeed be 0 anyways can you do this now?

minatsukisaya95 · Answer

Wow, that is really helpful. Thank you so much. :-))