This isn't homework but I didn't think that it warranted its own thread.

Can someone please tell me the probability of flipping a fair coin 100 times and having it come up heads 50 times (the ordering doesn't matter)?

Thanks!

edit:
Two more...
And, what's the probability of it coming <50 heads? (That is, the probability of 51 or more tails?)

And, what's the probability of it coming <26 heads? (That is, the probability of 75 or more tails?)

THANKS!

Exactly 50 times or at least 50 times?
If exactly, it would have to be 50%

Flip a coin 100 times. What is the probability that exactly 50 heads comes up?

50% is definitely the wrong answer.

Of course...nm

7.96 for exactly 50
46.02 for less than 50

ty sir...and for <25?

0,00000090500131% for <25

Hello all. This isn't homework but probably fits in this thread.

I have been doing some analysis on scoring and conceding goals when playing a man down in soccer and having calculated values for the mean goals scored per 90 minutes 10vs11 and 11vs11 I was told I can do a t-test to see whether the results are statistically significant. I did and got:

which SigmaPlot told me were both successful (I didn't know whether to do a paired or unpaired test so did both). My question is how do I interpret the p-value? Using the unpaired result, would it be accurate to say that I can be 99.9% sure that the result is statistically significant? How would you phrase the p-value of 0,0012.. in a sentence in layman's terms?

Thanks.

Not hw, but just curious. Is this a functional full adder? Would you consider it "efficient"? Apologies for crappiness of pic.

Yes, failure. Add a third AND between red & blue, then connect its output to an OR with the dark purple line (coming from the brown/pink OR), throw an OR between those two outputs, then put that into the NOT->AND->OR->Q set.

Now are we cool or did I just make 5 from 2+2?

I was wondering if someone could help me with a question. If we have a fleet of 800 vehicles, of which 11% of those have automatic transmission, and 43 of those vehicles are then stolen, all of which have manual transmission, what is the probability that this is a random occurance?

Is it just 0.89^43?

Thanks in advance

I would assume that's how you calculate it. You probably wouldn't have to calculate removing one at a time (11% will increase).

You havent given enough information sadly. Ill assume you're asking "given the above robbery has happened, what is the probability the robbers were stealing random vehicles (as opposed to specifically manual transmission vehicles)." We cannot get a numerical answer for this from the information given, but we can get one in terms of X, the prior probability that if u were to be robbed, the robbers would be after manual vehicles.

You want Prob(X | all cars stolen were manual), which is equal to X/(X+(1-X)Y), where Y is the probability of hitting 43 manuals randomly, which would be simliar to your above number but because of the lack of replacements a bit off. Thats the probability it wasnt accidental, so 1 minus that will be the probability it was

I think we can assume they were stealing at randon

For the question you have to do it in steps

712/800*711/799*710/798*.......

You can simplify this using factorials

eg 10!/6! = 7*8*9*10

It depends on how you think they were stolen. If they were taken by 40 different non-collaborators, obviously you have to re-consider the probability. Otherwise, if it was just a random number generator and it printed a list, then his formula holds.

That is a good point, I just read it as 'Over the course of a year....' or some such situation

Hey, I am writing a large report in LaTeX and I am using statistical program R. I know that there is a Latex-package or something with which one can insert results from R in to Latex. Can anyone give me any info on this?

He asked "what is the probability that it is random". How can we assume the fact that we are trying to find the probability for? That is nonsensical.

Your answer is correct for "if they are stealing at random, what is the probability they would only steal manual cars" (which is my Y term), which might be what was meant, but is very different to what was actually asked.

EDIT: And numerically, what you wrote (if that is what was wanted) comes out as 0.00652225

pretty simple calc 1 question, i figure.

if lim x-->a f(x) is DEFINED (i.e. there is no gap in the graph), does the limit exist?



does lim x --> 2+ exist?

hope i make sense and ty

the limit x--> 2+ exists.

it goes to 1, the function is a polynomial so you can just fill the limit in the function.

the limit does not exist btw if the upper and lower limit do not give the same value. Say for example you have:



the limit exists because the limit of the upper and lower part are the same even though the function value does not correspond to the value the limit gives you.
In your case the upper and lower limit are not the same and thus the limit in that point does not exist.

btw i do not understand the other question, if it is defined it exists because they are one and the same right? a limit must be defined to exist and a if it exists it is defined imo.

Anyone with a good understanding of linear algreba can you help me with this past exam question, my lecturer won't put solutions up for another month and ive been racking my brains trying to do this question. I think ive missed an important lecutre when he's gone through a question like this. Any help would be much appreciated.

Part i) is just expanding and substituting in the definitions for things. You use the orthogonality condition a couple of times and it should come right out.

Substitute the sum in for p(x) and do the same thing that you did for i) for the first part of ii). It'll be exactly the same, but you'll have a term cancel.

Then use say to compare the two and come up with some relation between fk and pk.

Need help with this question, i can get the problem into strum-liouville standard form but dont now how to show its self adjoint.




In my notes i have the followng formula to show its self adjoint but not sure how its done



Any help would be much appreciated!!

What does the symbol "Š" mean in the context of this sentence?

Substitute in for the integrals and use integration by parts. It might be easier to show that the integral u(Lv)-(Lu)v from [0,1] is zero. Since you have the definition of L, it should be pretty straight forward.