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KiRa [710]
3 years ago
15

Please help im on a test!!! Brainiest will be marked!!!

Mathematics
2 answers:
vredina [299]3 years ago
8 0

Answer: 15 square feet

Step-by-step explanation:

Multiply 3 x 1.25. This gives you the area of the rectangle which is 3.75 in. It is a scale model where every in is equal to 4ft. Multiply 3.75 by 4. 15ft is the answer.

laila [671]3 years ago
4 0

Answer:

answer is in the sbs explanation

Step-by-step explanation:

1.5625

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A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the
Anon25 [30]

Answer:

Part a

The maximum likelihood estimator of p, is the sample proportion,  \bar p=\frac{x}{n}

And the proportion of the estimate at n=25 and x = 3  is 0.12.

Part b

The maximum likelihood estimate from part (a) is an unbiased estimator.

Part c

The maximum likelihood estimate of the probability is 0.5277.

Step-by-step explanation:

a)

The likelihood function is, L(p;x) =\frac{n!}{x!(n-x)!}p*(1- p)^{n-x}

Applying log on both sides:

\log L(p;x) =\log\frac{n!}{x!(n-x)!}+x\log p+(n-x)log(1-p)

Find the differentiation of log L with respect to P and equate to zero to find the MLE for .

\frac{d}{dp}\log L(p,x)=\frac{x}{p}-\frac{n-x}{1-p}\\\\=\frac{x}{p}-\frac{(n-x)}{1-p}\\\\=x(1-p)-(n-x)p=0\\=x-xp-np+xp=0\\=x-np=0\\=x=np\\=\bar p=\frac{x}{n}

Calculate the estimate of the function if n=25 and x = 3.

\bar p=\frac{x}{n}\\\\=\frac{3}{25}\\\\= 0.12&#10;

Hint for next step

The MLE for the population proportion is the sample proportion and there is a 0.12 proportion of estimate at n = 25 and x = 3  

b)

Consider  

E(\bar p)\\\\E(\bar p)=E(\frac{X}{n})\\\\=\frac{1}{n}E(X)\\\\=\frac{1}{n}(np)(since\, E(X)&#10;=np)\\\\=p

Since E(\bar p)=p&#10;, the maximum likelihood estimate from part (a) is an unbiased estimator.

Hint for next step

Based on the part (a) calculation, since it is proved that , the maximum likelihood estimate is unbiased estimator for population proportion

(c)

Calculate the maximum likelihood estimate of the probability (1-p)^5.

By the Invariance property of MLE, to find the MLE of (1-P)^5, the MLE of p can be used.

That is, the MLE of (1-p)^5 is (1-\bar p)^5

Therefore,

MLE of the probability,

(1- p)^5 = (1-\bar P)^5\\\\=(1-\frac{3}{25})^5\\\\=(1-0.12)^5\\=(0.88)^5\\=0.5277

7 0
3 years ago
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