# Tagged Questions

32 views

### Rearranging equation with algebra

I'm having a difficult time showing that the two are equivalent: $2(x_1-\theta)(1+(x_2-\theta)^2)+2(x_2-\theta)(1+(x_1-\theta)^2) = 2(\bar{x}-\theta)(1+(x_1-\theta)(x_2-\theta))$ I have multiplied ...
24 views

### Calculating optimum values of $u$ and $m$ from $\mathbb V(\bar {y_2}\prime)=\frac{S_2^2(n-u\rho^2)}{n^2-u^2\rho^2}$

I have to find optimum sample size in sampling on two occasions. Suppose that the samples are of the same size n on both occasions. In selecting the second sample, $m$ of the units in the first ...
32 views

### Linear fit with Least Squares: what is going wrong?

I'm trying to do a Least Squares best fit for {1,2},{2,1},{3,3}. Unfortunately, my final formula continues to be wrong. As my final formula, I'm getting $y=\frac{1}{7}+\frac{13}{14}x$ - instead of - ...
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### -ln(0.1) equalling to ln(10)?

I am having quite a headache wrapping my head around this solution. I do not understand the first line where they get lambda = ln(10) from statement to the left. Somebody please explain this to me. ...
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### Evenly spreading study over 20 days?

Want to study $8$ hours a day, and $4$ hours on exam days. Want to study all exams exactly the same amount of time total. Exams in $10$,$13$,$19$,$20$ days from start. What is the daily ...
35 views

### Probability of three non-disjoint events(likely trivial)

This should be a trivial problem at this point, so it is embarrassing to ask, but here it goes: If I have the probabilities(of just these regions of a venn diagram, given by): ...
25 views

### How to measure how many % is done

Let's say that 100 people are going to two exams. They must pass both. In the first exam, 20% of people go forward to the next exam. In the 2nd exam, 50% of people complete and therefore complete the ...
32 views

So, I am computing something seemingly simple involving complex gaussians and constants, but I am getting a big contradiction in my calculations. The setup: Let $C$ be a complex constant, that is, ...
54 views

### $Pr(X+Y \geq \frac{\pi}{2})$

I want to find $Pr(X+Y \geq \frac{\pi}{2})$ for joint pdf $f_{X,Y}(x,y) = x \cos y, 0 \lt x \lt \frac{\pi}{2}, 0 \lt y \lt x, 0$ otherwise. I believe I have found conditional pdf of $Y$ given $X=x$ ...
74 views

### derivation of simple linear regression parameters

I know there are some proof in the internet, but I attempted to proove the formulas for the intercept and the slope in simple linear regression using Least squares, some algebra, and partial ...
121 views

### maximum likelihood - estimate $\sigma^2$ in $N(0,\sigma^2)$

Prove, using maximum likelihood, the estimation of $\sigma^2$ where $X$ is $N(0,\sigma^2)$ There is no real statistics involved, just algebra and finding partial derivatives, so I tagged it algebra ...
23 views

### Prove easy sum relationship

I want to understand the proof of how to estimate variance from the Normal distr, using the method of moments. It boils down to simple algebra. I can't understand why I tried to prove it like this ...
35 views

### Trouble solving these two equations

I'm doing a homework on uniform distribution and they gave me then mean and the standard deviation. I figured I had to solve for a and b to get min and max values. But when I try to solve for a and ...
43 views

### Proof using binomial coeff

I don't understand the step between left side and right side of my ? I
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### Modeling viral growth

I'm trying to forecast the viral growth for a website I'm developing. I've arrived at some monthly growth rates I can expect per month, the difficulty is I'd like to model my growth per week instead. ...
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### Mean and median of a linear piecewise pdf

I am studying for a test and I was wondering what is the mean and median of any linear piecewise pdf and why. Also just so you know p.d.f is probability density function.
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### Extending Completing the square to expressions of$(x+y+z)^2$

We all know expressions such as $x^2+14x+49 = (x+7)^2$ because it is easily recognizable as a perfect square. What about a expressions in the form of $x^2+2xy+2yz+2xz+y^2+z^2=(x+y+z)^2$ The question ...
62 views

### Finding aggregate score from incomplete data

\begin{align} n & = \text{number of reviews}\\ x & = \text{review score}\\ \bar{x} & = \text{aggregate score} \end{align} I have a specified number of reviews for a product, I have ...
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### How do I apply this probability transformation formula?

This is a simple formula but I'm struggling with it. I want to apply $$f_{Y} (y) = \frac{\left(f_{X}(\sqrt{y})+ f_{X}(-\sqrt{y})\right)}{\sqrt{2y}}$$ to $f_{x}(x)= \frac{1}{3}$ for $-1<x<2$, ...
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### How can i simplify the following term to get the right side?

$$\sum_{h=1}^{L}\frac{W_h^2S_h^2}{n_h}=\frac{1}{n}\sum_{h=1}^{L}{(W_hS_h)}^2$$ where, $n_h=\frac{n}{\sum_{h=1}^{L}N_hS_h}N_hS_h$ $\quad\text{and}\quad$ $W_h=\frac{N_h}{N}$ $\quad\text{and}\quad$ ...
69 views

### What is the fastest method for factoring this

I want the square root of $.09e^{-2t} + .24e^{-t} +.34 +.24e^t + .09e^{2t}$ I need this to find the moment generating function given it's product with itself (the product of two identical moment ...
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### $\exp(1i * 2 * \pi * (1:K) / K)$ to create clockwise format.

I was reading the documentation of R about text. here in the example : ...
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41k views

### How to calculate percentile? Is it possible to get 100 percentile?

How do we calculate percentile? I think it should be calculated as: P = Total number of candidates L = Number of candidates whose marks are below yours ...