BEC'S methods questions

[Collin Li]

Nice find. I remember this question in Essential, and I also found out what they meant at the time

[Glockmeister]

And if we had continued with where Mao was going, we would've divided by zero...

OH NOES.

[Mao]

And if we had continued with where Mao was going, we would've divided by zero...

OH NOES.

why don't you tell that to HIS FACE

jks jks

[excal]

steady state matrices are simply, when the next state is the same as the current state.

when a markov chain is expressed as a transition matrix:

, where S are your states. (the transition matrix need not to be restricted to 2x2, but for this case it will do)

steady-state is such that , i.e. when probability stop changing. this is your "overall" probability in the "long run"



this gives us simultaneous equations



so, using either [1] or [2] in conjunction with [3] to solve, you can now find the probability of events at steady-state.

Since when was THIS on the course?

(I only learnt this at TSFX...lol - and not even the steady state stuff, just transitions. Steady state came in 2nd year uni...)

[cara.mel]

^ since you do methods cas

[excal]

Oh. Right.

[bec]

The time taken to get to school is normally distributed with a standard deviation 7 minutes. If the probability that a student takes more than 50 minutes to get to school is 0.2375, find the mean time to travel to school.

How do I do this? I'm thinking it has something to do with the formula , but I get confused with what z and x represent.
Thanks

[Collin Li]

Translate this to the standard normal so we can extract some information about and according to:







Using invNorm(, we get: (to 4 d.p.)

(rounded up)

[bec]

Um..what's invNorm( ??

Your explanation helped me work it out a similar way anyway (just subbed in z=0.7625 and x=50 into the equation and solved for - is this right?)

Do you think that is an issue that I don't know it? I have a CAS calculator, and I've been taught to use Stat/List or the program "Probably" for probability distributions...Can I use them in this case, or am I going to have to learn how to use InvNorm?
Thanks

[Collin Li]

Hmm... I'm not sure, I use the TI-83 interface.

= invNorm(a) is the function, where:

[bec]

Sorry, I edited my post while you were replying - I got the answer anyway...does that method seem alright to you?

[Mao]

um..what's invNorm( ??
Is that an issue that I don't know it? I have a CAS calculator, and I've been taught to use Stat/List or the program "Probably" for probability distributions...Can I use them in this case, or am I going to have to learn how to use InvNorm (very quickly, considering I have a SAC)?
Thanks

since you have the Stat/List program, in Home screen, press Catalog, then F3 (to take you to the FlashApps functions)
you should be able to find a range of functions useful for probability here:

binompdf(n,p,x) *using binompdf(n,p) gives a very interesting output, you should try it also
binomcdf(n,p,lower bound,upper bound)

normcdf(lower bound,upper bound,μ,σ) *using normcdf(lower bound,upper bound) will give the result according to the standard normal distribution, i.e. treating the lower and upper bounds as Z scores.
invnorm(area,μ,σ) *using invnorm(area) will give the result according to the standard normal distribution, i.e. a Z score

[Mao]

Um..what's invNorm( ??

Your explanation helped me work it out a similar way anyway (just subbed in z=0.7625 and x=50 into the equation and solved for - is this right?)

no, Z in this case (as coblin has calculated using his calculator) is 0.7144, whereas the cumulative density function up to z=0.7144 (i.e. the probability) is 0.7625. These are two different quantities.

to get from z to cumulative density function, use the normcdf function from negative infinity to the z score
to get from the probability (area) to the z score, use the invnorm function. however, you need to beware that the invnorm function takes the area as from negative infinity, so sometimes you may need to manipulate the probability you are given.

[bec]

Yeah, not really understanding...
My calc is Ti-89, and it sounds like my flashapps are slightly different to yours (thanks for pointing them out though, they seem good)
My options are normPdf, normCdf or invNorm...do you (or does anyone else) happen to know how I could use any of these functions to answer the question?

[Collin Li]

invNorm probably does what I explained in this post:

Hmm... I'm not sure, I use the TI-83 interface.

= invNorm(a) is the function, where:

You can also put extra parameters into it, like:

For a normally distributed random variable with mean and standard deviation :

= invNorm(), where