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2 years ago

15

What is greater 9,000 g or 8 kg

1 answer:

nikdorinn [45]2 years ago

5 0

9000 grams is bigger

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Let X1,..., Xn be a simple random sample from a distribution with density function Svorvo-1 O<331 fx (2:0) = otherwise where

scZoUnD [109]

Answer:

The method of moment (MOM) estimator as: $\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}$

$\overline X = \dfrac{4}{9}$

$\mathbf{\hat {\theta} =\dfrac{16}{25} }$

Step-by-step explanation:

From the question, the correct format for the probability density function is:

$fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.$

where θ > 0 is an unknown parameter.

(a) The MOM estimator can be calculated as follows:

$E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx$

$E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx$

$E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0$

$E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }$

suppose E(X) = $\overline X$

Then;

$\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }$

$\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}$

$\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}$

making $\dfrac{1}{\sqrt{\theta}}$ the subject of the formula, we have:

$\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1$

$\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}$

$\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}$

squaring both sides, we have:

The method of moment (MOM) estimator as: $\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}$

b) If the observations are $\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}$

Then,

$\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}$

$\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}$

$\overline X = \dfrac{\dfrac{8}{6}}{3}$

$\overline X = \dfrac{8}{6} \times \dfrac{1}{3}$

$\overline X = \dfrac{8}{18}$

$\overline X = \dfrac{4}{9}$

Finally, the point estimate of the estimator $\theta$ is

$\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}$

$\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}$

$\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}$

$\mathbf{\hat {\theta} =\dfrac{16}{25} }$

6 0

3 years ago

What is the mid point of the x-intercepts of f(x)=(x-2)(x-4)?

Oxana [17]

Answer:

The x-int.s are (2, 0) and (4, 0) so the midpoint will be (3, 0).

3 0

3 years ago

Read 2 more answers

Find the number of palindromes between 10,000 and 99,999 that are divisible by 25

Cerrena [4.2K]

<u><em>20</em> palindromes exist that qualify this criteria rigorously</u>

Examples:

52025, 52125, 52225, 52325, 52425, 52525, 52625, 52725, 52825, 57975 etc.

3 0

2 years ago

Which of the following has two bases?<br> A. prism<br> B. pyramid<br> C. line<br> D. plane

Margaret [11]

A. Prism

A prism has two bases

3 0

3 years ago

If AB=12 cm and BC =13 cm then AC = 25 cm

Maru [420]

Answer:

AB=12

Hope this helps!

8 0

2 years ago