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2 years ago

8

What numbers are members of both the set of whole numbers and the set of integers?

1 answer:

hammer [34]2 years ago

5 0

all postive whole numbers

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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

G(x)=3x-2;find g(7)

mixas84 [53]

G(7)=3(7)-2 || g(7)=19

3 0

2 years ago

Read 2 more answers

Need Help ASAP). □ ABC is transformed to □ DBE. I posted a picture of the design and questions A, B, and question C. ( Will Mark

salantis [7]

Answer:

A)A reflection can be used to create DBE

B)The Angles are congruent, as the transformation was rigid, which preserves angle measure and side length.

C)All the angles are corresponding to the second figure as well as the sides. (name all the sides and angles that are corresponding)

Ex: ABC=DBE

Hope this helps!

P.S. Stay Safe!

-Andrew-OUT!

3 0

2 years ago

Read 2 more answers

What is 1.75 divided by 5.25

Diano4ka-milaya [45]

Answer:

0.333333333

Step-by-step explanation: its goes on forever never stopping

3 0

2 years ago

Read 2 more answers

Find the areas of the sectors formed by ABC

Amanda [17]

Answer:

33.51 in^2

Step-by-step explanation:

Find the area of the circle:

A = πr^2

A = π * 8^2

A = 64π = 201.06 in^2

Find the area of the 60 deg slice:

A * 60/360 = 33.51 in^2

Leave a thanks and mark brainliest if this helped

Leave a thanks and mark brainliest if this helped

6 0

2 years ago