Can some help me what really is the formula of the standardized precipitation index and how will it be computed?
I am thinking of using the index to classify the 40 years into dry year, average year , or wet year using total annual rainfall data. I understand that SPI is an index based on the...
May I ask what is needed to be computed in order to compare the estimators of the population mean \bar{y}_{N}, in terms of accuracy? That is to compare the multivariate ratio estimator \bar{y}_{RM} with the Y-only estimator \bar{y}_{n} in terms of accuracy.
Let X be a single observation from the density f\left(x;\theta\right) = \theta x^{\theta -1}I_{(0,1)} (x), where \theta > 0. What is the P\left[X \geq \frac{1}{2} |\theta > 1|\right]?
Please help me structure the solution of this problem
Homework Statement
The number of sales made by a used car salesman, per day, is a Poisson random variable with parameter \lambda. Given a random sample of the number of sales he made on n days, what is the most powerful test of the hypothesis Ho: p = 0.10 versus Ha: p = 0.25, where p is the...
P\left[\frac{X_{1}+X_{2}}{2} > 0.99\right] = \int^{1}_{0}\int^{0.98}_{0} 1 dx_{1}dx_{2} = 0.98
Is this right?
If I double integrate the joint pdf with when X1 goes from 0 to 1 and X2 goes from 0 to 1, I got P\left[\frac{X_{1}+X_{2}}{2} > 0.99\right] = 1.
I think it is not right because...
Homework Statement
Given that X is a uniform random variable on the interval (0, \theta), we might test Ho: \theta = 1 versus the alternative H_{1}: \theta = 2 by taking a sample of 2 observations of X and rejecting Ho if \bar{X} > 0.99. Compute \alpha2. The attempt at a solution
\alpha =...
It is defined that the population variance is S^{2}= \frac{1}{N-1}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2} or \sigma^{2}= \frac{1}{N}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2}.
Also that the V\left[\bar{y}_{n}\right] = \frac{N-n}{N}\frac{S^{2}}{n} = \left(\frac{1}{n} -...
May I ask how to find the E\left(ln x\right) and Var\left(ln x)?
The X_{i} are random sample from the f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right) where \theta > 0.
I need the information in finally solving the Cramer-Rao lower bound for the variance of...
Okey. Thank you statdad for your reply.
But, I will be very happy if you will tell me how to find an unbiased estimator of this \kappa\left(\theta\right).
Oh, here's what I've done.
\frac{nr}{\hat{\lambda}}= \sum x
Solving for \lambda:
\hat{\lambda} = \frac{rn}{\sum x} = \frac{rn}{n \bar{x}} = \frac{rn}{n \frac{r}{\lambda}} = \lambda
Is this not right?
Homework Statement
For a random sample X_{1}, ..., X_{n} from the Poisson distribution, find an unbiased estimator of \kappa\left(\theta\right) = \left(1 + \theta) e^{-\theta}.
The Attempt at a Solution
I know that the pmf of Poisson distribution is f\left(x; \theta\right) =...
Alright, thank you for all your replies. I've tried figuring them out. Here are the outcomes. Kindly check if these are right.
\frac{d}{d\lambda} log L\left(\underline{y}; r, \lambda\right) = \frac{nr}{\lambda} - \sum y
Equating the derivative above to zero results to...
Homework Statement
Let X_{1}, ... , X_{n} be a random sample from f\left(x; \theta\right) = \theta x^{\theta - 1} I_{(0, 1)}\left(X\right), where \theta > 0.
a. Find the maximum-likelihood estimator of \theta/\left(1 + \theta\right).
b. Is there a function of \theta for which there...