Be Pro in T-Statistic in No Time: Tips & Tricks

Let ${X i} \sim N (i θ, 1)$ for $i = 1, . . . ., n$ be an independent, but not identically distributed sample. Check that $T = \sum_{i} X_{i}$ it is a sufficient statistic for $θ$ .

tramolatzqvg 2022-11-03

Finding the Expected Value of $T =$ $\sum X_{i}^{2}$

drzwiczkih5a 2022-11-03

Let $X i$ be a random variable distributed as $N (i, i^{2}), i = 1, 2, 3$ . As-sume that the random variables $X_{1}, X_{2}$ and $X_{3}$ are independent. Using only the three random variables $X_{1}, X_{2}$ and $X_{3}$ give an example of a statistic that has a $t$ distribution with two degrees of freedom.

Barrett Osborn 2022-11-02

We're given a random sample of $X_{1}, X_{2}, . . . ., X_{n}$ from a distribution with a pdf of
$f (x; θ) = θ^{x} (1 - θ), x = 0, 1, 2, . . . .$ and $0 < θ < 1$
Show that that $T n = \sum_{i = 0}^{n} X_{i}$ is a complete sufficient statistic for $θ$ .

Alberto Calhoun 2022-11-02

Derive the Cramer von Mises test statistic
$n C_{n} = \frac{1}{12 n} + \sum_{i = 1}^{n} {(U_{(i)} - \frac{2 i - 1}{2 n})}^{2}$
where $U_{(i)} = F_{0} (X_{(i)})$ the order statistics

Uriah Molina 2022-11-02

Derive an expression for the $p$ -value using a test with test statistic $T = \sqrt{n} ({\bar{X}}_{n} - θ_{0}) / σ$

assupecoitteem81 2022-11-02

Let $X 1, . . ., X n$ be independent and identically distributed with density $P_{θ} (x) =$
${\begin{cases} 2 x / θ^{2} & for 0 \leq x < θ \\ 0 & else \end{cases}$
Demonstrate that $m_{n} = m a x (x_{1}, . . ., x_{n})$ is a sufficient statistic .

ajanlr 2022-10-30

We know that if $T$ is a sufficient statistic for $θ$ then $f (T)$ is a sufficient statistic for $f (θ)$ if $f (.)$ is a one -one function. But,what if $f$ is not one one? For example, in case of Bernoulli $(p)$ ,how to find the sufficient statistic for $p (1 - p)$ ?

cousinhaui 2022-10-30

Difference between Factorization theorem and Fischer-Neymann theorem for t to be sufficient estimator of $θ$

Kymani Hatfield 2022-10-30

The standardized sample mean will be of the form $\frac{\bar{x} - μ}{s / \sqrt{n}}$ , which because we are using an estimated standard error of the mean vs. the standard error of the mean would imply we use the $t$ -statistic, right?

Pellagra3d 2022-10-30

Let $X$ be a random variable having the negative binomial distribution with
$P (X = x) = (\begin{matrix} x - 1 \\ r - 1 \end{matrix}) p^{r} (1 - p)^{x - r}, x = r, r + 1 \dots$
where $p \in (0, 1)$ and $r$ is a known positive integer.
Find the UMVUE of $p^{t},$ , where $t$ is a positive integer and $t < r$ .

Izabelle Lowery 2022-10-29

Let $X \sim B e r (n_{1}; p), Y \sim B e r (n_{2}; p^{2})$ , where $X$ and $Y$ are independent. Find a minimal sufficient statistic $T$ and, using a nontrivial function, show that it is not complete.

ebendasqc 2022-10-29

Show that in a simple linear regression $y = X β + ϵ$ , when the mean is subtracted from any feature (i.e. some column of the matrix $X$ ), the $t$ -statistics of all the non-intercept coefficients do not change.

Marilyn Cameron 2022-10-29

If $\bar{X}$ and $S^{2}$ be the usual sample mean and sample variance based in a random sample of $n$ observation $N (μ, σ^{2})$ and $T = \frac{(\bar{X} - μ) \sqrt{n}}{S}$ ` prove that $C o v (\bar{X}, T) = σ \frac{\sqrt{n - 1} Γ (\frac{n - 2}{2})}{\sqrt{2 n} Γ (\frac{n - 1}{2})}$

Deon Moran 2022-10-29

Hypothesis testing: how do you call the variable that is being hypothesized about?

Maribel Vang 2022-10-28

Suppose that $X_{1}, \dots, X_{n}$ are n i.i.d. random variables from the Poisson distribution truncated on the left at $0.$ . Find the UMVUE of $P (X_{1} = 1) .$ .

Maribel Mcintyre 2022-10-28

Sufficient statistic based on a random sample of size n where the pmf is $P_{θ} (X = x) = c (θ) 2^{- x / θ}$

varsa1m 2022-10-28

For a Mann-Whitney test do we use the $T$ value from the smallest sample size as the test statistic or the smallest $T$ value?

Ayanna Jarvis 2022-10-27

Let $X_{1}, X_{2}, X_{3}$ be a iid sample of the Bernoulli $p$ distribution. Consider the statistic $T = X_{1} X_{2} + X_{3}$ . Show that $T$ is not sufficient for $p$ .

ndevunidt 2022-10-27

Suppose $X \sim N (μ, σ^{2})$ . I know that $T (X) = (\bar{X}, S^{2})$ is a complete sufficient statistic for $μ, σ^{2}$ if $μ, σ^{2}$ are unknown. But if $μ, σ^{2}$ is known, is $S^{2}$ still a complete statistic of $σ^{2}$ ?

T-Statistics can help you answer questions about the mean of a population given a sample. This is done by using equations to calculate if the mean of the population is significantly different from a specific value, or to compare two distinct samples to each other. T-Statistics can provide powerful insights and answers, and are a great tool for anyone who wants to analyze a sample to draw conclusions. With the help of a t-statistic, you can answer questions such as "is the average of this sample significantly different from this given value?". T-Statistics can provide helpful information and give you the tools necessary to make effective decisions.

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