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2 years ago

I NEED HELP with problems 4,6,and 8

Mathematics

2 answers:

Snezhnost [94]2 years ago

7 0

#4
1 mile = 5280 ft'
2 miles = 5280 * 2 =10,560 ft

#6
1 quart = 2 pints
2 3/4 = 2.75 quarts = 2.75 * 2 = 5.5 pints

#8
1 yard = 3ft

40ft = 40/3 = 13.33 yards

Monica [59]2 years ago

6 0

2) 32
4) 10560
6)5.5.......................

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Answer:

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Step-by-step explanation:

For this case we have a random sample $X_1 ,X_2,...,X_n$ where $X_i \sim N(\mu=\theta, \sigma)$ where $\sigma$ is fixed. And we want to show that the maximum likehood estimator for $\theta = \bar X$ .

The first step is obtain the probability distribution function for the random variable X. For this case each $X_i , i=1,...n$ have the following density function:

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The likehood function is given by:

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Assuming independence between the random sample, and replacing the density function we have this:

$L(\theta) = (\frac{1}{\sqrt{2\pi \sigma^2}})^n exp (-\frac{1}{2\sigma^2} \sum_{i=1}^n (X_i-\theta)^2)$

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Now if we take the derivate respect $\theta$ we will see this:

$l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)$

And then the maximum occurs when $l'(\theta) = 0$ , and that is only satisfied if and only if:

$\hat \theta = \bar X$

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