Help please due at 9

A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and

mr Goodwill [35]

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

$\mu = \frac{3X_{1} + 4X_{2} }{8}$

Now

Bias for the estimator = E(μ bar) - μ

= $E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5$

= $\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5$

= $\frac{3(4.5) + 4(4.5)}{8} - 4.5$

= $\frac{13.5 + 18}{8} - 4.5$

= $\frac{31.5}{8} - 4.5$

= 3.9375 - 4.5

= - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

= Var(μ bar) + [Bias(μ bar, μ)]²

= $Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136$

= $\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136$

= $\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136$

= $\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136$

= $\frac{1}{64} [7(57.76)}] } + 0.3136$

= $\frac{1}{64} [404.32] } + 0.3136$

= $6.3175 + 0.3136$

= 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

6 0

3 years ago

Match each expression in the left column with the correct product in the right column.

lesya692 [45]

Answer:

-6

-6i

6i

6

Step-by-step explanation:

1) √4 . √-3 . √-3

$\sqrt{4} = 2$

$\sqrt{-3} . \sqrt{-3} = (\sqrt{-3})^2$

$\sqrt{4} . (\sqrt{-3})^2 = 2 \times -3 =$ -6

2) √-4 . √-3 . √-3

$\sqrt{-4} = 2i$ .

Therefore, $\sqrt{-4} . \sqrt{-3} . \sqrt{-3} = 2. \sqrt{-1} \times -3 = 2i \times (-3) =$ - 6i

3) √4 . √3 . √-3

$\sqrt{4} = 2$

$\sqrt{3} . \sqrt{-3} = (\sqrt{3})^2 . \sqrt{-1}$

$\implies 2 \times 3i =$ 6i

4) √4 . √3 . √3

$\sqrt{4} = 2$

$\sqrt{3} . \sqrt{3} = (\sqrt{3})^2 = 3$

Therefore, √4 . √3 . √3 = 2 . 3 = 6

5 0

3 years ago

50 points for answer.

noname [10]

Answer:

Point C: (4, 0)

Step-by-step explanation:

Parallelograms are quadrilaterals with two pairs of parallel sides, this means they will have the same slope between two line segments.

point slope form between two points: y - y1 = m (x - x1)

point A (2, 6) and D (4,4):

slope: point form, 6 - 4 = m(2 - 4)

2 = -2m

m (slope) = $\frac {2}{-2}$ = $\frac {Change in X position}{ Change in Y position}$

now that you know the change in position, apply this to vertice B to get the position of the final vertice.

B(2, 2)

C (2 +2, 2-2) = C(4, 0)

The final position of C vertice for parrallelogram A(2,6), B(2,2), D(4,4) will be C(4,0)

5 0

2 years ago

Read 2 more answers

Estimate the answer by rounding. 453 + 158 + 204 + 555 + 361

son4ous [18]

I would say 1700 , I hope this helps

4 0

3 years ago

Read 2 more answers

I WILL GET A ZERO SO PLEASE HELP! THANKS!!!

Setler79 [48]

M=6 is the correct answer
Plz mark brainliest

4 0

2 years ago

Read 2 more answers