2
votes
1answer
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 ...
0
votes
1answer
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 ...
0
votes
2answers
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 - ...
2
votes
1answer
76 views

-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. ...
1
vote
1answer
66 views

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 ...
0
votes
2answers
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): ...
0
votes
0answers
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 ...
1
vote
2answers
32 views

Contradiction with complex gaussians…

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, ...
1
vote
1answer
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 $X=x$ ...
1
vote
2answers
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 ...
1
vote
2answers
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 ...
0
votes
1answer
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 ...
0
votes
1answer
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 ...
1
vote
2answers
43 views

Proof using binomial coeff

I don't understand the step between left side and right side of my ? I
0
votes
1answer
46 views

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. ...
0
votes
1answer
99 views

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.
1
vote
4answers
58 views

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 ...
2
votes
1answer
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 ...
0
votes
0answers
25 views

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 $-1<x<2$, ...
0
votes
1answer
28 views

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, $n_h=\frac{n}{\sum_{h=1}^{L}N_hS_h}N_hS_h$ $\quad\text{and}\quad$ $W_h=\frac{N_h}{N}$ $\quad\text{and}\quad$ ...
0
votes
2answers
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 ...
0
votes
0answers
34 views

$\exp(1i * 2 * \pi * (1:K) / K)$ to create clockwise format.

I was reading the documentation of R about text. here in the example : ...
1
vote
2answers
91 views

Why add one to the number of observations when calculating percentiles?

The CFA Quantitative Methods book uses the following formula for finding the observation in a sorted list that corresponds to a given percentile $y$ in a set of observations of size $n$: $(n + ...
1
vote
2answers
114 views

Using integrals to prove that the mean of the sampling distribution is the population mean

Let the random variables $X_1, X_2, \dots X_n$ denote a random sample from a population. The sample mean of these random variables is: $\overline{X}=\frac{1}{n}\sum\limits_{i=1}^{n}X_i$ I would like ...
0
votes
1answer
23 views

statistical range of a measurement

DoI need to find out the range? How to solve this problem? hints or canonical answer will be helpful for me.
0
votes
0answers
25 views

Determining Range

$X_i\sim^{iid}N(0,1);\quad i=1,2$ so $x_i$ ranges from $-\infty$ to $\infty$. Now $Y=X_1^2+X_2^2$ so $y$ ranges from $0$ to $\infty$. But how $Z=X_2$ is ranges from ($-\sqrt y$) to $\sqrt y$ ?
0
votes
1answer
47 views

Marginal distribution of $P$

Joint distribution of $P$ & $Q$ is $$f_{P,Q}(p,q)=\frac{1}{2\sqrt{(2\pi)}\sigma}\exp[-\frac{1}{2}{(\frac{\frac{p+q}{2}-\mu}{\sigma})^2}] \times\theta\exp[-\theta(\frac{p-q}{2})],\quad ...
4
votes
2answers
150 views

$4$ women and $2$ men are being interviewed. Find the probability the women will be interviewed first.

My Calculations: $$\frac{4}{6}\times\frac{3}{5}\times\frac{2}{4}\times\frac{1}{3} = \frac 1 {15}$$ Is that correct?
1
vote
1answer
72 views

cumulants of non-central $\chi^2$ distribution

Cumulant generating function is defined by logarithm of moment generating function. $$K_X(t)=\log M_X(t)$$ Let $X$ be a non-central $\chi^2$ variate with parameters degrees of freedom, $n$ and ...
0
votes
2answers
27 views

A small calculation .

How $\sum_{k=0}^n (-1)^n\times(-1)^{n-k}=\sum_{k=0}^n(-1)^k$ i got it $\sum_{k=0}^n(-1)^n\times(-1)^{n-k}=\sum_{k=0}^n(-1)^{2n-k}$ And is that $\mathbb E[\mathbb E(X)]=\mathbb E(X)$ ?
2
votes
2answers
88 views

Why differentiating a function is similar to differentiating its log function?

$f(6;p)=\binom{25}{6}p^6(1-p)^6,\quad 0\le p\le1$ I have three questions: $(1)$To find the relative maxima of p, the process is to take the derivative of the function with respect to $p$ equal to ...
3
votes
4answers
320 views

How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$

How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$ i have tried to do that by the following procedure: $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2$ ...
2
votes
1answer
98 views

Expanding the square in the variance

$\newcommand{\var}{\operatorname{var}}$ In the Pattern Recognition book of Bishop, I'm reading the following statement, that I don't fully understand. The variance of $f(x)$ is defined by ...
2
votes
0answers
40 views

Comparing two or more sets of sequences

I have observed nurses during 400 episodes of care and recorded the sequence of surfaces contacts in each. I categorised the surfaces into 5 groups 1:5 and calculated the probability density ...
0
votes
1answer
114 views

Relationship between three variables

I have three variables $r$, $p$, and $ w$. The $w$ is weight, $r$ is distance, and $p$ is the number of people. Morover, I have $$r = aw^b,~~p = ae^{bw}$$ where $a$ and $b$ are constants. Given a ...
0
votes
1answer
2k views

Method of Moments on a Uniform distribution (a,b)

Given that $x_1,x_2,...,x_n$ are i.i.d. random variables drawn from a Uniform distribution over $(a,b)$ (with $a<b$ and both are unknown), I hope to estimate $a$ and $b$ using the method of ...
0
votes
1answer
27 views

Basic expression mangling question

I am looking at the solution of a physics/statistics hybrid exercise, and I can't figure out how one expression step took place. I have that $${dx \over dt} = gt$$ $$T = \sqrt{2h \over g}$$ where ...
0
votes
1answer
163 views

Computing for n in this given (Statistics)

This question came from an exam on statistics from one of our clients (we are a tutorial center). According to USA Today (March 17, 1997), women made up 33.7% of the editorial staff at a local TV ...
0
votes
1answer
178 views

Algorithm to Get a Product score based on rating

I am trying to device a algo for product score. Here are the inputs User rates a product on 5 different criteria out of 10 Each criteria has a different weightage with all adding up to 100% There ...
0
votes
1answer
90 views

Weighted Values

I hope to be able to get some assistance here, I tried reading through some of the posts, however, they are far above my math abilities..so I apologize if this is a re-post or this is a basic ...
0
votes
1answer
115 views

Calculate Growth Rate of Balance

I am trying to create a formula to calculate the growth rate for a balance. My variables are as follows: $B{\scriptsize0} =$ beginning balance $A =$ Dollar Increase for a given month ...
1
vote
0answers
76 views

Simultaneous equations for bacteria.

I would like to calculate the value of bacteria on 4 surfaces $i=\{1..4\}$. A person touches some of those 4 surfaces at random and a count is made on their finger after each surface contact ($x_i$). ...
1
vote
2answers
763 views

Geometric mean of a dataset containing $0$s

We are taught that geometric mean (GM) should only be applied to a dataset of positive numbers, and some insist that it should be strictly positive numbers. However, I have seen people discussing the ...
1
vote
0answers
86 views

Solving $c(n, n-2) - p(n, 2) = 7 - n$

To help with a friends homework, I was asked how to solve this equation for $n$: $$c(n, n-2) - p(n, 2) = 7 - n$$ Having no further information about what c and p are supposed to be (and they don't ...
0
votes
1answer
57 views

Growth rate question

Something grows at an annualized rate of 5% for 4 months and then declines at an annualized rate of 4% for the next four months. What would be the annualized growth rate over the entire 8 month ...
-2
votes
2answers
138 views

Please solve for X

I messed up the equation last time I asked this - Can someone please solve this function for X? $Y = \displaystyle 0.5\:a\:\text{erf}\left(\frac{x-b}{c\sqrt{2}}+.5\right)+d$ When I solve for Y with ...
6
votes
5answers
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 ...
5
votes
4answers
1k views

Geometric mean never exceeds arithmetic mean

This was a mathematical induction question proposed in a textbook, and I've exhausted multiple approaches (proving RHS - LHS > 0, splitting the fraction, fractional exponents, etc.) The geometric ...
2
votes
1answer
76 views

Maximum combined 1st through nth highest combinations of ai + bi

I have two sets (a,b) of data and I am restricted to using the values in the sets once and only once when they are combined. For example, the 2nd highest value possible from a data set of a{3,2} ...