Recent content by Portishead

I posted this post by mistake, please delete this post.

I'm using these lecture notes as a guide, just so you can know what assumptions were made for this problem: http://ocw.jhsph.edu/courses/MethodsInBiostatisticsI/PDFs/lecture1.pdf http://ocw.jhsph.edu/courses/MethodsInBiostatisticsI/PDFs/lecture2.pdf I have no idea to be honest.

It's intuitively zero and E1 and E2 are mutually exclusive/disjoint events? If either ## P(E_1) ## or ## P(E_2) ## were the maximum, intuitively wouldn't that be less than or equal to the sum of both probabilities since ##P(E_i) \geq 0##? I just don't know how to formally show my conjecture. Is...

All I can think of is that: 1) ## 0 \leq P(E_1 \cap E_2) \leq 1 ##, by definition...

Thanks for the hint! So when n=2, ##\max_{1,2} P(E_i) \leq P(\cup_{i=1}^2 E_i)## ##=P(E_1)+P(E_2)-P(E_1\cap E_2)## ##\leq P(E_1) + P(E_2) ## Then, assume for when n=k , ##\max_{i\in N} P(E_i) \leq P(\cup_{i=1}^k E_i)## Define ##Q= \bigcup_{i=1}^k E_i## and let n=k+1. Thus, ##\max_{i\in N}...

When n=2, my conjecture is that ##\max_{1,2} P(E_i) \leq P(\cup_{i=1}^2 E_i) \leq P(E_1)+ P(E_2) ## by intuition, but I don't know how to write this formally... My induction hypothesis is as follows, right? Then, for all positive integers n, ##\max_{i\in N} P(E_i) \leq P(\cup_{i=1}^n E_i)##

Homework Statement Prove that[/B] P(\cup_{i=1}^n E_i) \geq \max_i P(E_i) (1) for n≥1 Homework Equations I know that P(\cup_{i=1}^n E_i) \leq \sum_{i=1}^n P(E_i). The Attempt at a Solution I know when n=1, trivially P(E_1) \geq \max_1 P(E_1) =P(E_1). So I was hoping I could use induction to...

rl.blat, can you take an ordinary derivative of that expression? t and t1 are different variables? Also, uh I solved the problem. I minimized v-passenger=x-train(t')-x-passenger(6)/(t'-6)=.20(t')^2/(t'-6) where t' is the time she gets on the train. That function has a relative minimum at t'=12 s...

So, wouldn't it be the other way around? Train(t)=.20t^2; Passenger(t)=v(t-6)

I don't think so, as it is not given.

Homework Statement A train pulls away from a station with a constant acceleration of 0.40 m/s^2. A passenger arrives at a point next to the track 6.0 s after the end of the train has passed the very same point. What is the slowest constant speed at which she can run and still catch the train...

Do you need help with #13 still?