Recent content by nossren

Yes, I realize that has to be true for it to be correct, but I am just confused about the signs. My book (Sears and Zemansky's) mentions some sign conventions in relation to Kirchhoff's voltage law (see picture). So why is it + rather than - ?

Homework Statement Assume you have a fully charged capacitor with initial condition V(0) = V_0 connected in series to two resistors R_1 and R_2. Derive an expression for the voltage over the capacitor with respect to time. Homework Equations 1. Kirchhoff's voltage law \sum_n V_n = 0 2. Ohm's...

Yes, the amount of balls in the "bucket" can be assumed to tend towards infinity, therefore the probability is constant. However, what I have learned is that when you have a sample with distribution N(μ, σ²) you want to construct a reference variable with some distribution ##N(0,1),\ t(n-1),\...

The variance for X is then, according to my book, V(X) = nqp = 50\cdot(1-0.15)\cdot0.15. How can I justify going from N to Bin? edit: p was supposed to be 0.15, mixed it up with another exercise

I redid the calculation using the definition $$ \sqrt{V(X)} = \sqrt{\sum_k (k-\mu)^2p(k)} = \sqrt{(9-7.5)^2\cdot 0.149} \approx 0.579 $$

Homework Statement Suppose you have a bucket containing a lot of balls with different colors. You randomly pick 50 balls, 9 of which are red (X = 9, where X ~ N(μ, σ²)). The probability of picking a red ball is 15%. From this you want to construct a 95% confidence interval for the standard...

bump also meant to say (V/V_0)^n

I did that, and now I get (after dropping higher power terms) $$ (V/V_0)^{n-1} \cdot (1 - v/V + v/V_0 -2v/V + 2v/V_0 - ...) = (V/V_0)^{n-1} \cdot (1 - (1+2+3+...)v/V + (1+2+3+...)v/V_0) $$ which leaves me with a (V/V_0)^(n-1) in front of the wanted expression. I don't see how to get around...

I'm still not following. I solved it for the numerator, which yielded 1-(1+2+3+...)v/V. By reverse engineering (12), the denominator must be 1-v/V_0. But since the numerator was divided by V to obtain 1-v/V the denominator must too. How do I solve it for the denominator? $$ V_0/V - v/V $$

Would you mind elaborating on the taylor expansion?

I'm currently reading about thermodynamics and osmosis and I happened to stumble across this paper. There is one thing I don't really understand, though.. In chapter 8 the author wishes to give a thermodynamic explanation of the osmotic pressure so I've been reading through the derivation. When...

When you put it that way it doesn't seem to make sense. If the variables takes on discrete values, talking about the limit of the random variable would be like looking at the limit of a constant, which is pointless.

Nowhere is the nature of the random variable stated. However, doesn't it take on countably infinite values? Correct me if I'm wrong.

All that is said about X_n is $$ \mathbb{P}(X_n = k/n) = \frac{1}{n+1} $$ for k = 0,1, ..., n, but I thought this was implied since it's a uniform distribution. I'm just confused what they mean with the notation of the distribution.

Sorry. $$ M_X(t) = E(X) = E(e^{tX}) $$ I calculated the MGF of X_n to $$ \frac{e^t-1}{t} $$ by integrating, but I'm not sure the calculations are correct. Edit: I too am uncertain of what they mean by U(0, 1/n, ..., (n-1)/n, 1). I haven't seen the notation anywhere else in the book, only in the...