Bucket's Questions

[Mao]

to find the conditional probability, it's the probability of BOTH events occuring, divided by the probability of the condition

i.e. in this case, X has to be >12 as well as >8, which simplifies to X>12 (because 12>

hence,
for the purpose of methods, if you are using an 84 or older calculator, use a very large number in place of infinity, such as 99999. This will give a fairly accurate answer, as f(x) gets quite small as it approaches to infinity. if you are using 89 or later, you are blessed with the "inifinity" key.

how to analytically evaluate those two integrals are covered in the first year course at uni =]

[Mao]

think of a number line:

Code: [Select]


--------|8----|12--------->
        xxxxxxxxxxxxxxxxxxx (x>8)
              xxxxxxxxxxxxx (x>12)

the intersection of the two is fairly obvious: x>12

[Collin Li]

how to analytically evaluate those two integrals are covered in the first year course at uni =]

What? You can get an exact value with Methods techniques:

[bucket]

thanks both of you!
and thank god i have an 89 =]

and wow :S

[shinny]

What? You can get an exact value with Methods techniques:

I think he's referring to 'subbing in' the infinities, which normally can't be done, but I think we're meant to know how to do that in methods with an integral like that, since it's e to a negative power, and when you sub in infinity, it just becomes zero (well..approaches).

[Mao]

[bucket]

find A and B if

[Collin Li]

Two unknowns: A and B

Two pieces of information:
1. The probability density function has a total area of 1
2. The mean is 12

Hence, you can solve this. Write out statements 1 and 2 in mathematical speak -- evaluating integrals and simplifying, and then use simultaneous equations (if necessary) to find A or B, then substitute it into the other equation to find the other constant.

[Collin Li]

1.



2.



Dividing equation (2) by equation (1) yields:

[excal]

I might just splice in how number two was derived:

Remember that the expected value of a probability density function (pdf) is .

Because we are bound by the pdf: , we have to restrict our domain. We also know that expected value (mean) is 12.



For , using :







And then you reach coblin's step 2.

[bucket]

yeah, thanks both of you for your help in that last question.

Now I have NO idea how to approach this one:



b. Find the value of a which gives the standard deviation of 2.

In part a. of the question it made me find that

[Collin Li]

and








Therefore:

(Substituting in)

Also,

So:





From the domain, since

Hence:

[bucket]

thanks heaps =]

[bucket]

mmm.
how do you find the standard deviation of a normal distribution curve by just looking at it?? :S
i know the mean where the maximum occurs...

[Collin Li]

I guess roughly the 99.7% range is from 120 to 150 in the first one (coz that's where the curve practically touches the x-axis -- it doesn't but it looks like it), so hence 3 standard deviations from the mean is , and hence the standard deviation is 5.

You'd never get anything like this on the exam though, haha.