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3 years ago

Which statement about kites is false ?

Mathematics

1 answer:

Strike441 [17]3 years ago

8 0

The worng answer is [b]
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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

Find the number that makes each statement true.

Harrizon [31]

1) 30
2) 800
3) 500
4) 4,000
5) 9
6) 600
7) 7,000
8) 200,000
9) 2,000 * 10 = 20,000. 20,000 * 10 = 200,000.

6 0

3 years ago

6. The variable x and y vary directly, and y = 40 when x = 5. Which equation relates the variables?

valkas [14]

Answer:

The equation relates the variables is y = 8x ⇒ D

Step-by-step explanation:

If x and y vary directly (y ∝ x), then y = k x, where

k is the constant of variation

k can be found using the initial value of x and y

∵ The variable x and y vary directly

∴ y ∝ x

→ By using the rule above

∴ y = k x

∵ y = 40 when x = 5

∴ The initial values of x and y are x = 5 and y = 40

→ Substitute them in the equation above to find k

∵ 40 = k(5)

∴ 40 = 5k

→ Divide both sides by 5

∵ $\frac{40}{5}$ = $\frac{5k}{5}$

∴ 8 = k

→ Substitute the value of k in the equation above

∴ y = 8x

∴ The equation relates the variables is y = 8x

5 0

2 years ago

What number would go in the blank? (3 • 5) • 2 = 3 • (__ • 2) 10 5 2

tester [92]

Answer:

Step-by-step explanation:

It's the one that's missing.

Hope I helped!

Please mark Brainliest!

7 0

2 years ago

Read 2 more answers

Question 8

borishaifa [10]

Answer:

y = ½x

Step-by-step explanation:

y = ½x

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7 0

3 years ago