Homework Statement
A die is biased such that the probability of getting a six is 1/4. The die is rolled 2000 times. Let X be the number of sixes obtained. Find,
a) the mean of X
b) the standard deviation of X, leaving your answer as a surd.
Homework Equations
The Attempt at a...
Ok let's just solve this real quickly.
See if f(x) converges from 0->1.
Using the same, if g(x) converges, we'd be using the same steps, except from 0 to 1 now. This would give you
-1/e + 1. Given that they are all constants (its approaching a value), we know it converges.
I know this is...
Yeah, It is, I figured it out as you can see haha. However, the f(x) <= g(x) is only for x>=1, we don't worry about x=0 -> x<1 because.. hmm, I'm honestly not sure.
Hmm, a comparison test does seem interesting. So let's try this out.
Let f(x)=e^{-x^2}
and Let g(x)=e^{-x}
Where 0\leq{f(x)}\leq{g(x)}
Given the comparison test, if g(x) is convergent, we can assume that f(x) is also convergent.
\stackrel{lim}{b\rightarrow\infty}\int_0^b{e^{-x}}...
Yes, I realize what you say, so:
lim (b-> \infty) \int_0^b{e^{-x^2}}
I realize that e^\infty is infinity, therefore, making it divergent. However, that's wrong because I have to integrate it first. Hence my question, how would I approach integrating {e^{-x^2}}
Homework Statement
Test for convergence:
b. \int_0^\infty{e^{-x^2}}
Homework Equations
Any method you choose to approach the problem in order to test for convergence.
The Attempt at a Solution
First, I attempted to integrate the problem. However, I am not exactly sure how to...
Thanks for the infiltration test. I talked to my teacher and he enjoyed the idea of the water infilitration. I think I'm probably going to do this test, along with measuring altitude, wind speed in the area, and moisture. Personally, I didn't like the moisture test, as it has little to do with...
I am performing the Group IV Experiment in approximately 3 days, and I needed some last-minute help and suggestions towards what I am doing. My group is examining two ecosystems, one with and one without a river. We will view how different water and soil factors affect the biodiversity of the...
#2
As for #2, how much has Juanita traveled in 45 minutes?
How much will she have traveled once you have caught up to her? (in 1 hour and 45 mins)
that should help
qk
Oh I get it!
So f(x)=\ln \frac {x(x-2)}{(x+2)(x-2)}
So f(x)=\ln \frac{x}{x+2}
Awesome, part A solved. Now find the inverse..
Give me a sec here
Argh, the only way i know of obtaining inverses is by flipping x and y's.. here it seems a tidbit different. I know that:
The domain of the...
Im sorry, I left an ln x out, for some reason I typed \lnx and it appeared as nothing. Should I still factor the denominator? ~ I had chow mein with chicken :D
Homework Statement
The function f is defined for x>2 by f(x)=\ln x+\ln(x-2)-\ln(x^{2}-4)
a. Express f(x) in the form of (\ln\frac{x}{x+a})
b. Find an expression for f^{-1}(x)
Homework Equations
..The Attempt at a Solution
Well, I simplified it to:
f(x)=\ln(\frac{x^{2}-2x}{x^{2}-4})
I can't...