All Questions
Tagged with sum self-study
17
questions
0
votes
0
answers
26
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PDF of difference of uniform distributions [duplicate]
Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation.
Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
2
votes
2
answers
384
views
How to check these sequences generated by i.i.d random variables are martingales?
Let $\{Y_n\}_{n\geq 1}$ be a sequence of independent, identically distributed random variables.
$P(Y_i=1)=P(Y_i=-1)=\frac12$
Set $S_0=0$ and $S_n=Y_1+...+Y_n$ if $n\geq 1$
I want to check if the ...
- 1,216
1
vote
0
answers
357
views
Probability of sum of sequences of integers
Let K be a positive integer.Suppose that the integers 1,2,3,...,3k+1are written down in random order.What is the probability that at no time during this process, the sum of the integers that have been ...
- 1,216
4
votes
1
answer
130
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Question regarding the distribution of sum of random variables
Let $X_1, ... X_n$ be i.i.d random variables that have an exponential distribution with parameter $\theta$. So we know that $\sum X_n \sim \Gamma(n, \theta)$.
This makes sense by working backward. ...
- 889
1
vote
1
answer
164
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How to evaluate a summation equation containing a random variable?
I'm trying to find:
$$\Pr(B = 0)$$
Where:
$$B = \sum_{i=0}^N b_i$$
And:
\begin{align}
N &\thicksim \mathrm{Poisson}(\lambda=10) \\
b_i &\thicksim \mathrm{Geometric}(p=0.8)
\end{align}
...
- 11
1
vote
0
answers
801
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Expectation of absolute value of sum of 2 random variables with conditions
Suppose $X$ and $Y$ are random variables such that
$E(X+Y)=E(X-Y)=0$ and
$Var(X+Y)=3$ and
$Var(X-Y)=1$ then how to show that $E(|X+Y|)\leq \sqrt3$
Guidelines asap would help me
thanks.
- 29
2
votes
1
answer
3k
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how to Differentiate the kNN formula?
I am going through a book on statistical learning and ran into a problem concerning k nearest neighbor methods. The book says that using least squares to determine optimal k will lead to $k=1$. I ...
- 454
1
vote
0
answers
99
views
How to show that the summation of the product of residuals and fitted values equal 0?
I would like to show that $\sum e_i\hat{Y}_i$ = 0 with $\hat{Y} = HY$, $H$ - hat matrix and $e$ - the residuals $(I-H)Y$.
So far, I've gotten
$$\sum e_i\hat{Y}_i = e^T \hat{Y} = ((I-H)Y)^T HY$$
...
- 615
2
votes
1
answer
1k
views
Subset Sum with Constraints
I'm taking a look at what I have identified as being a subset sum problem.
I have around 650 potential values which could form part of my single sum value. I've began looking into the typical ...
- 123
2
votes
1
answer
417
views
difference between independent binomial variables
Let $X_1$ and $X_2$ be independent random variables where $X_1 \sim \mathrm{Bin}(m, 1/2)$ and $ X_2 \sim \mathrm{Bin}(n,1/2)$.
How can we prove that $X_1 - X_2 + n \sim \mathrm{Bin}(m + n ,1/2)$?
Can ...
- 663
3
votes
1
answer
505
views
How to find the joint distribution of sums of Poisson random variables
I am trying to determine the joint distribution of two sums of Poisson random variables.
Let's say $X \sim \text{Pois}(\lambda_{1})$, $Y \sim \text{Pois}(\lambda_{2})$, and $Z \sim \text{Pois}(\...
- 33
3
votes
1
answer
66
views
Proving a property of $(n-1)s^2$
I would appreciate your help as I climb the stats learning curve!
I want to prove the following:
"Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$
Then ...
- 33
4
votes
1
answer
169
views
Using Poisson distribution to evaluate summations
I'm interested in how to use a Poisson distribution to evaluate $\sum\limits_{x=0}^\infty \frac{(x^2-x+1)(2^x)}{x!}$
I see that this is similar to the general pmf form of $\frac{2^{x}}{x!}$. My ...
- 85
2
votes
1
answer
2k
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Expectation of cube of summation of independent random variables
Where would I begin on this problem?
I know I begin with pulling $c^3$.
Where would I go from there?
And I know that $\mathbb{E}[X] = x_1p_1 + .... x_n p_n$
I'm stuck on the rest, however.
- 21
1
vote
2
answers
219
views
Sum of combination
My problem is:
Evaluate:
$$\sum_{i=0}^n i{n \choose i}$$
I only know that $$\sum_{i=0}^n{n \choose i} = 2^n$$ not so sure when an "i" is added.
What is the step of this evaluation?
- 113