Which expression is the prime factorization of 180X²Y? *

Suppose that E(θˆ1) = E(θˆ2) = θ, V(θˆ 1) = σ2 1 , and V(θˆ2) = σ2 2 . Consider the estimator θˆ 3 = aθˆ 1 + (1 − a)θˆ 2. a Show

katen-ka-za [31]

Answer:

Step-by-step explanation:

Given that:

$E( \hat \theta _1) = \theta \ \ \ \ E( \hat \theta _2) = \theta \ \ \ \ V( \hat \theta _1) = \sigma_1^2 \ \ \ \ V(\hat \theta_2) = \sigma_2^2$

If we are to consider the estimator $\hat \theta _3 = a \hat \theta_1 + (1-a) \hat \theta_2$

a. Then, for $\hat \theta_3$ to be an unbiased estimator ; Then:

$E ( \hat \theta_3) = E ( a \hat \theta_1+ (1-a) \hat \theta_2)$

$E ( \hat \theta_3) = aE ( \theta_1) + (1-a) E ( \hat \theta_2)$

$E ( \hat \theta_3) = a \theta + (1-a) \theta = \theta$

b) If $\hat \theta _1 \ \ and \ \ \hat \theta_2$ are independent

$V(\hat \theta _3) = V (a \hat \theta_1+ (1-a) \hat \theta_2)$

$V(\hat \theta _3) = a ^2 V ( \hat \theta_1) + (1-a)^2 V ( \hat \theta_2)$

Thus; in order to minimize the variance of $\hat \theta_3$ ; then constant a can be determined as :

$V( \hat \theta_3) = a^2 \sigma_1^2 + (1-a)^2 \sigma^2_2$

Using differentiation:

$\dfrac{d}{da}(V \ \hat \theta_3) = 0 \implies 2a \ \sigma_1^2 + 2(1-a)(-1) \sigma_2^2 = 0$

⇒

$a (\sigma_1^2 + \sigma_2^2) = \sigma^2_2$

$\hat a = \dfrac{\sigma^2_2}{\sigma^2_1+\sigma^2_2}$

This implies that

$\dfrac{d}{da}(V \ \hat \theta_3)|_{a = \hat a} = 2 \ \sigma_1^2 + 2 \ \sigma_2^2 > 0$

So, $V( \hat \theta_3)$ is minimum when $\hat a = \dfrac{\sigma_2^2}{\sigma_1^2+\sigma_2^2}$

As such; $a = \dfrac{1}{2}$ if $\sigma_1^2 \ \ = \ \ \sigma_2^2$

4 0

4 years ago

Identify if the expressions below are polynomials or not for each of them.

monitta

The polynomials can´t contain:

-Variables in the exponents of the terms.
-Variables in the denominator.
- Negative exponents.
-Fractionals exponents.
-The variables cant be as radicals.

Therefore:

a) It is a polynomial (The variable is under a radical)
b) It is not a polynomial.
c) It is a polynomial.
d) It is not a polynomial. (It has a variable in the denominator).
e) It is a polynomial.
f) It is not a polynomial. <span> (It has a </span><span>variable in the denominator).</span>

4 0

3 years ago

Pls answer I will mark brainliest

Flura [38]

Answer: The answer is 36ft³, or 2916ft.

5 0

3 years ago

Read 2 more answers

The results of a poll show that the percent of people who want a new restaurant is in the interval (24%, 38%) . There are 112,48

iris [78.8K]

Change the percents to decimals (by moving the decimal 2places to the left)
(.24, .38)

Multiply each by 112,483.
(.24x112483, .38x112483)
(26,996, 42,744). You can’t have decimals because people are whole numbers. So round to the nearest whole number

8 0

3 years ago

What is the y intercept of the graph of 4x + 2y = 12

yan [13]

Answer:

the y intercept is 6

Step-by-step explanation:

Step 1: Add -4x to both sides.

4x+2y+−4x=12+−4x

2y=−4x+12

Step 2: Divide both sides by 2.

2y /2 = −4x+12 /2

y=−2x+6

Points (3,6)

x intercept is 3 and y intercept is 6

4 0

3 years ago