Tagged Questions
0
votes
1answer
12 views
Basic question on the transformation of Exponential distribution.
Why central moments coincide for random variables
$V\sim E(a,h)$ and $Y\sim E(h)$
where a=location parameter
h= scale parameter.
0
votes
0answers
21 views
Convolution of exponential distribution.
let $Y_1\sim E(λ_1 )$ and $Y_2\sim E(λ_2 )$. $Y_1$ & $Y_2$ are independent random variables
let $V=Y_1+Y_2$
show that the pdf of $p_V(x)$ = $\frac {\exp[-(x/λ_1)] - \exp[-(x/λ_2)] } ...
2
votes
1answer
40 views
Find the limiting distribution
Find the limiting distribution for $n\rightarrow \infty \text{ of} \prod\limits^n_{i=1}X_i$. Given is that $f(x)=\frac{1}{2x\sqrt{2\pi}}e^{-\frac{1}{8}(\ln x-\theta)^2}, x\geq 0$.
0
votes
0answers
16 views
Survival Analysis Partial Likelihood
Part of a medical statistics course is on Survival Analysis. We are introduced to the Cox Proportional Hazard model and then move on to look at partial likelihood $L(\beta)$. There is little on what ...
1
vote
1answer
22 views
expected value of random variables
Take two random variables $X=a+bX_0$ and $Y=c+dY_0$, and define $T=X-Y=\mu+\sigma Z$ where $\mu$ is the mean of $T$, $\sigma$ its standard deviation and $Z$ is a standardized random variable with mean ...
0
votes
1answer
18 views
please prove the following proof related to F distribution.
Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively.
Then show that
...
1
vote
1answer
23 views
How do I work out what percent of my customers will be girls and what percent will be boys?
I know that 33.3333% of all girls questions would buy my product and that 80% of all boys questioned would buy it.
What i don't know is how to work out is statistically what percentage of our ...
2
votes
1answer
42 views
Cramer-Rao Lower Bound
Assume that $X_1,X_2,\ldots,X_N\sim N(\mu,2^2)$ and $Y_1,Y_2,\ldots,Y_M\sim N(0,\sigma^2)$.
a)Find the Cramer-Rao Lower Bound (CRLB) for the variance of the unbiased estimators of $\mu$.
b)Find the ...
2
votes
1answer
27 views
simplifying an asymptotic expression
I have this expression in a statistics book, namely $nh(f(x) +o(1)+O_p(1/\sqrt{nh}))$. Where $f$ is a density function. Now, this expression is equal to $nhf(x)\{1+o_p(1)\}$. Note, that $n\to ...
2
votes
1answer
30 views
How do I sum two Poisson processes?
If we have a Poisson Process $Y$ with intensity $\lambda$ and a Poisson Process $X$ with intensity $\mu$, where $X$ and $Y$ are two independent Poisson processes. How can I find the process ...
1
vote
1answer
57 views
Maximum likelihood estimators, hypergeometric and binomial
I'm trying to solve a two part problem. The set up is as follows: consider a bag with $\theta$ red marbles and $7-\theta$ blue marbles, with $\theta$ being unknown. Let $x$ denote the number of red ...
1
vote
1answer
71 views
Rao-Blackwell unbiased estimator geometric distribution
I'm looking at review questions and having trouble with this one!
Let $X_1,\ldots,X_n$ be i.i.d. geometric R.V.s with the pmf: $(1-p)^{x-1}p$, for $x=1,2,\ldots$ and $0<p<1$.
I need to use ...
0
votes
1answer
47 views
Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$
Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$.
This should be a really easy question but I somehow cannot seem to get the right answer. My ...
1
vote
1answer
40 views
Bayes theorem for calculation with personal probabilities
I'm completely stuck on some homework I have and can't figure it out.
The task is to calculate the probability of a bus being late conditional on the weather being snowy and bus driver being ...
0
votes
2answers
41 views
to calculate standard deviation using mean and sample size
Given the mean as 1336 and sample size as 24, how to calculate standard deviation when the deviation scores and sample figures are unknown.
-1
votes
1answer
68 views
Some Algebra 2 help [closed]
The table shows the distance and costs of flights for a given airline with the same starting destination and different ending destinations.
Distance (miles) vs Cost($)
1281 473
2796 683
790 ...
-1
votes
0answers
20 views
Probability that difference sample mean from population mean is 1.96 sd [closed]
Probability that difference sample mean from population mean is 1.96 sd
a)68%
b)95%
c)47/5%
d)99%
2
votes
3answers
64 views
Homework Question. Joint Probability Distribution.
Here is the question.
The joint PDF of X and Y is given by $f_{XY}(x,y) = {\frac 14} e^{-|x|-|y|}$. Find $P(X \le 1 ,and, Y \le 0)$
Solving the problem I first found the marginal probabilities of X ...
0
votes
0answers
30 views
Homework Help. Probability Density Functions.
$X$ is $N(10,1)$. Find $f(x|(x-10)^2 < 4)$
This is a homework question. I can only figure out that X is normally distributed with mean 10 and variance 1.
Can you please explain what is meant to ...
-1
votes
0answers
21 views
Which of the following describes there is no the significant differences between the parameters?
Which of the following describes there is no the significant differences between the parameters?
1)power of a test
2)confidence level
3)The null hypothesis(H0)
4)The unlike hypothesis
-4
votes
1answer
27 views
What is the distance for 68% people grades?
In the normal distribution, if mean $=12$ and sd $=2$, what is the distance for $68\%$ people grades?
$10-14$
$10-12$
$8-12$
$2-10$
0
votes
0answers
42 views
Generalized Likelihood Ratio Test and Hypothesis Testing
Below is a question from a review sheet on an upcoming final that I am really struggling with. Any help is greatly appreciated!
Let $Y_1, Y_2,...,Y_8$ be a random sample from the uniform ...
0
votes
1answer
50 views
prove likelihood
I have the following problem:
The data in the following table relate to the classification of 11 208 physical particles into five types.
...
0
votes
1answer
24 views
simple question about probability density function
A really simple one - I don't know why I got stuck with this \=
$$ 1-P(x>\dfrac{-ln\alpha+\Theta}{\Theta}) $$
When $f(x)=2xI_{0<x<1}$
0
votes
1answer
35 views
HELP Distribution of the Minimum of two random variables
Well Let $Y$ be a random variable that could be discrete or continuous and $M$ a positive constant random variable Find the distribution of $S$$=$$min${Y,M}
My progress so far is :
$p($S ...
0
votes
1answer
24 views
Approximating Chi squared distribution
A machine in a heavy equipment-factory produces steel rods of length Y , where Y
is a normally distributed random variable with mean 6cm inches and variance $\frac{1}{4} cm^2 $. Thecost C of repairing ...
0
votes
1answer
37 views
Uniform distribution inside a binomial distribution
Suppose that three contestants on a quiz show are each given the same question,
and that each answers it correctly, independently of the others, with probability P. The
diculty P of the question is ...
0
votes
1answer
26 views
Question regarding Type II Error in Hypothesis Testing
The following is a homework problem and I am not really sure where to begin or how find what the question is asking.
Suppose that one observation from the exponential pdf $f_{y}(y)=\lambda ...
1
vote
1answer
31 views
Hypothesis Testing a small sample for the binomial parameter p
The following is a question from a homework set that I truly do not understand how to even begin.
The following is a Minitab printout of the binomial pdf $p_{x}(k) {9 \choose k}(0.6)^k(0.4)^{9-k}$, ...
0
votes
0answers
19 views
Power Curves from Normal Distribution.
The following is a homework problem that I cannot figure out because I am having trouble finding the Type II error.
Construct a power curve for the $\alpha = 0.05$ test of $H_0:\mu = 60$ versus $H_1: ...
2
votes
1answer
29 views
Monte Carlo Rejection Sampling Method
I have the following passage from a set of lecture notes I am working on that I would like to understand a little better.
$\underline{\text{Algorithm for Rejection Sampling}}$:
Given two densities ...
0
votes
0answers
39 views
Question about Infinite Markov chains
Do 2 Markov chains $\left\{X_n\right\}^\inf_{n=0} $ and $\left\{Y_n\right\}^\inf_{n=0} $ with all of these properties exist so that the probability for infinite n values to maintain $X_n=Y_n$ is 0? ...
0
votes
0answers
49 views
something about property of Bernoulli random variables
Let $b_i, i=1, \ldots, n$ be Bernoulli random variables with probability $P(b_i=1)=2k/n,$ where $k\leq n.$
Show the following:
Let $\chi$ be an indicator function that $k$ out of $n$ of $b_i$ are ...
0
votes
2answers
50 views
Central Limit Theorem VS Normal Model
I just had a quick question regarding the Central Limit Theorem and Normal Model. I am in an elementary probability course and we have learnt that the CLT is as follows:
$$ Z = \frac{X_1 + X_2 + X_3 ...
1
vote
1answer
28 views
$X$ and $Y$ correlation coefficient of $2/3$ , find $\mathrm{Var}(3X − 5Y+ 7)$
I am trying to solve this simple problem but I realize that I am missing something. Here is the problem:
$X$ and $Y$ have correlation coefficient of $2/3$ and $\mathrm{Var}(X)=1$ and ...
0
votes
1answer
30 views
What is the sufficient statistic for this function?
$f(x)=\theta/x^2$ where $\theta<x<\infty$
Given that the likelihood is $lik(\theta)=\theta^n \prod x_i^{-2}$
It seems to me that $T(X)=\prod x_i^{2}$ is the sufficient statistic, but ...
0
votes
1answer
27 views
Confidence Intervals Homework help
I'm having trouble finding the right answer to this question:
If $H_0: \mu= 240$ is tested against $H_1: \mu < 240$ at the
$α= 0.01$ level of significance with a random sample of
twenty-five ...
0
votes
1answer
30 views
Question regarding Bonferroni correction
Prove the following version of the Bonferroni inequality-
$$P\left(\bigcap_{i=1}^kA_i\right)\ge1-\sum_{i=1}^kP(A_i^c)$$
When creating simultaneous confidence interval, what are $A_i$ and $A_i^c$?
...
0
votes
2answers
71 views
How to maximize this function? [duplicate]
The function is $lik(\theta)=\theta^n\prod_{i=1}^n x_i^{-2}$ where $\theta<x<\infty$
I am getting $0$ if I just take the derivative of the log of this function. I believe this has to do with ...
0
votes
2answers
62 views
Cumulative Distribution of X/Y
Let X, Y be independent exponential variables with rates $\alpha$, and $\beta$. Find the c.d.f. of X/Y.
So far, I let Z = X/Y.
I can then show $f_Z(z) = \int_{-\infty}^{+\infty} |x|f_{X,Y}(x,xz) ...
0
votes
0answers
33 views
Statistics: Using t-Table to Find Population Quantile
Use the probability table (https://dl.dropboxusercontent.com/u/8336578/final_tables.pdf) to find the 0.01 (top 1%) population quantile of the standard normal distribution. If this is not possible ...
1
vote
1answer
26 views
What is the difference between a zero-inflated and a zero-truncated poisson?
I'm trying to make sense of a question which uses a zero-inflated poisson model given by:
$$
f(x; \lambda,\omega) = \begin{cases} \omega + (1-\omega)e^{-\lambda} &\mbox{if } x = 0 \ \ \ \ \ \ ...
0
votes
1answer
39 views
Find the percentage of student “A Grade”
Score
less than $58$: F
$58$ to $66$: D
$66$ to $74$: C
$74$ to $82$: B
$82$ and above: A
Mean: $70$
Standard deviation: $8$
Find the percentage of student "A ...
4
votes
1answer
240 views
Partial sum of numbers
My TA gave today this question as a nice question to think about. He said its involves standard ideas of Probability theory and numbers. But, I don't even know how to start.
Let $x_1, \ldots, x_n$ ...
0
votes
0answers
31 views
Independent Normal Variables for measuring mass
Suppose the true weight of a standard weight is 10 grams. It is weighed twice independently. Suppose that the first measurement is a normal random variable X with E[X] = 10g and Standard Deviation ...
2
votes
1answer
31 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
...
1
vote
4answers
86 views
$P(T_2 \ge T_1)$ Exponentially distributed functions
I have a problem regarding probability.
The lifetime $T$ of a product is exponentially distributed.
Product 1 has expected lifetime: $F_1(t) = 1-e^{-t/1000} $
Product 2 has expected lifetime: ...
0
votes
0answers
37 views
expectation with Bernoulli random variables
Let $x\in R^n, x \geq 0$ and let $b_i, i=1, \ldots, n$ be $(0,1)$ Bernoulli random variables with $P(b_i=1)=p$. For $q\geq 1$ estimate from above
$$
E_{b_i}\left|1+x_ib_i\right|^q\leq ?, \quad i=1, ...
2
votes
4answers
70 views
Playing chess until one party wins
Players $A$ and $B$ decide to play chess until one of them wins. Assume games are independent with $P(A\text{ wins})=0.3$, $P(B\text{ wins})=0.25$, $P(\text{draw})=0.45$ on each game. If the game ends ...
1
vote
2answers
28 views
Probability of a sample size
At a fertilizer company, 20% of the bags coming off of the line are below the advertised label weight(underweight). If a random sample of fertilizer bags is taken and each bag is weighed until $1$ ...
