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3 years ago

The area of a square rug is 169ft^2. How long is each side of the rug?

Mathematics

1 answer:

jek_recluse [69]3 years ago

6 0

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{13 \: ft}}}}}$

Step-by-step explanation:

$\star{ \sf{ \: Area \: of \: a \: square \: rug \: ( \: A \: ) \: = \: 169 \: {ft}^{2} }}$

$\sf{ \underline{Finding \: the \: length \: of \: a \: square \: ( \: l \: )}}$

$\boxed{ \sf{Area \: of \: a \: square \: = \: {l}^{2} }}$

$\hookrightarrow{ \sf{169 = {l}^{2} }}$

$\hookrightarrow{ \sf{ {l}^{2} = 169}}$

$\hookrightarrow{ \sf{ \sqrt{ {(l)}^{2} } = \sqrt{169} }}$

$\hookrightarrow{ \text{length \: = \: 13 \: ft}}$

$\text{Hope \: I \: helped!}$

$\text{Best \: wishes !!}$

~ $\text{TheAnimeGirl}$

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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