All Questions
19 questions
3
votes
2
answers
242
views
Calculating $E[(\sum X_i)^4]$
Trying to figure where I'm going wrong with the following. My goal is to calculate var$(\bar X_n^2)$ using $E[(\bar X_n)^4]=\frac{1}{n^4}E[(\sum X_i)^4]$ given that $X_1,...X_n$ are iid with $EX_1=\mu,...
- 385
0
votes
0
answers
59
views
mean and variance
Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 1 when X = 1 and Y = 0 when X = 0. What is ...
- 1
1
vote
0
answers
26
views
Probability that both the mean and sample variance are both covered by their respective confidence intervals?
I am given the question: "What is the probability that both the mean is in its confidence interval for confidence level a and the variance is in its confidence interval for confidence level a?&...
- 11
0
votes
1
answer
281
views
Finding mean and variance of number of tosses needed to get exactly 2 heads
A coin with probability of getting head $0.6$ is tossed repeatedly till two heads appear. Let $X$ be the number of tosses needed to get exactly 2 heads. Describe the sample space. Find the mean and ...
- 175
2
votes
1
answer
86
views
When would the variance for a probability distribution give the same result as the standard equation?
Variance equation for a probability distribution:
$$
\sigma^2 = \sum_{i=1}^{N}(x_i-\mu)^2P(X=x_i)
$$
Standard variance equation:
$$
\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i-\mu)^2
$$
I understand that ...
- 123
0
votes
0
answers
55
views
How much compensation is needed to take on risk?
We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? ...
1
vote
0
answers
31
views
Understanding Covariance after Variance (visually)
2 Points i understood from variance derivation-
A) For calculating Variance we do not subtract (or mod add), but rather sum squared all points' differences from the mean.
B) Variance of 1,2,3 will be ...
- 11
8
votes
4
answers
3k
views
Is it possible for a distribution to have known variance but unknown mean?
Many tutorials demonstrate problems where the objective is to estimate a confidence interval of the mean for a distribution with known variance but unknown mean.
I have trouble understanding how the ...
- 208
4
votes
1
answer
2k
views
Convergence in distribution versus convergence of moments
Suppose we have that a random variable sequence $(X_n)_n$ converges in distribution to a law with mean $\bar{\mu}$ and variance $\bar{\sigma}^2$, or formally $X_n \stackrel{d}{\to} \mathcal{L}(\bar{\...
- 1,419
7
votes
1
answer
716
views
Mean and variance of $\tan(\mathcal{N}(\mu,\,\sigma^{2}))$
How could we find the mean and variance of $\tan(\theta )$ if $\theta \sim \mathcal{N}(\mu,\,\sigma^{2})$?
- 303
0
votes
1
answer
275
views
How to estimate the mean and variance of a Gaussian distribution variable? [closed]
I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
0
votes
1
answer
117
views
Summation of two Gaussian distributed data with different coefficient of mean and variance
I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them?
...
0
votes
1
answer
161
views
estimating the mean of constant + noise
(This is almost certainly covered in Statistics 101, but I missed that class..)
I have a real-world sampled signal $S[t]$ that is a constant $\hat{S}$ plus some noise $\epsilon[t]$. My goal is to ...
- 155
0
votes
1
answer
213
views
Do the location and scale parameters always control the mean/median/mode and variance, respectively?
Does a location parameter always control the mean/median/mode values of a PDF?
Does a scale parameter always control the variance of a PDF?
If the answer to any of the above questions is yes, then ...
- 115
-2
votes
1
answer
97
views
Representing a distribution of probabilities
I'm running a simulation where, for every iteration $i$, I get a detection probabilities $P_i$. Because of the law of total expectation, I think the overall detection probability (i.e. marginalizing ...
- 167
4
votes
0
answers
703
views
Expectation and variance of sample mean with random sample size
I have a question regarding sampling where the sample size itself is a random variable.
Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
- 41
1
vote
0
answers
26
views
Time-partitions of sample size
I am struggling with explain something I read in a Whitepaper. The essence is as follows.
Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X \...
- 11
1
vote
0
answers
1k
views
Mean and variance of call center data
I have a fairly involved homework question, I was wondering if I could get some help.
There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number of ...
- 133
4
votes
1
answer
851
views
Probability of average given mean and variance
For the life of me I cannot find a way to solve this question. Any help would be appreciated!
From past experience, a professor knows that the test score of students taking a final examination is a ...
- 41