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2 years ago

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Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is ap

proximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5λe−λ|x| for −[infinity] < x < [infinity]. The standard deviation is given as 39.8 km. (Round your answers to four decimal places.) (a) What is the value of the parameter λ?

1 answer:

Luda [366]2 years ago

3 0

Answer:

The value of the parameter is λ is 0.03553357

Step-by-step explanation:

Consider the provided function.

$f(x) = 0.5\lambda e^{-\lambda |x|}$ for −∞ < x < ∞.

It is given that standard deviation is given as 39.8 km.

Now we need to calculate the value of parameter λ.

The general formula for the probability density function of the double exponential distribution is: $f(x)=\frac{e^{-|\frac{x-\mu}{\beta}|}}{2\beta}$

Where μ is the location parameter and β is the scale parameter.

Compare the provided equation with the above formula we get.

$\lambda=\frac{1}{\beta}$ and μ = 0.

Standard deviation = √2β

$S.D=\sqrt{2} \beta\\\beta=\frac{39.8}{\sqrt{2}}\\\beta=28.1424$

Now substitute the value of β in $\lambda=\frac{1}{\beta}$ .

$\lambda=\frac{1}{28.1424}=0.03553357$

Hence, the value of the parameter is λ is 0.03553357

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At UF, there are always a few days between the end of classes and the beginning of final exams. These days are meant as a study

Natalija [7]

Answer:

This sample is not representative of all UF students, since those who are not local are not considered.

Step-by-step explanation:

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

However, the sample has to be representative

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected Buffalo residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

In this problem, we have that:

They conduct a phone survey (with local numbers selected at random from the student directory) calling people during "dead week". Will this sample be representative of all UF students?

They only call those students with local numbers.

However, in an university, it is expected that there will be a good percentage of non local students.

So this sample is not representative of all UF students, since those who are not local are not considered.

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2 years ago

Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package.

Arturiano [62]

Answer:

<u>A. When Rita started, she had 7 packages of saplings.</u>

<u>B. If we represent x (number of packages of saplings) on a number line graph, it will start on number 4 (number of packages Rita still has) then moves to the right to number 7, that is the number of packages when Rita started to plant.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of packages Rita started = x

Number of saplings per package = 5

Number of saplings planted by Rita = 15

Number of saplings left = 20

2. How many packages of saplings did she start with?

Number of packages Rita started = (Number of saplings planted by Rita + Number of saplings left)/Number of saplings per package

Replacing with the real values:

x = (15 + 20)/5

x = 35/5 = 7

<u>When Rita started, she had 7 packages of saplings.</u>

3. What would the solution look like on a number line graph?

If we represent x (number of packages of saplings) on a number line graph, it will start on number 4 (number of packages Rita still has) then moves to the right to number 7, that is the number of packages when Rita started to plant.

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2 years ago

The length of life of an instrument produced by a machine has a normal ditribution with a mean of 12 months and standard deviati

Zielflug [23.3K]

Answer:

a) $P(X$

And we can find this probability using the normal standard distirbution or excel and we got:

$P(z$

b) $P(7$

And we can find this probability with this difference:

$P(-2.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-2.5$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

a) less than 7 months.

Let X the random variable that represent the length of life of an instrument of a population, and for this case we know the distribution for X is given by:

$X \sim N(12,2)$

Where $\mu=12$ and $\sigma=2$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard distirbution or excel and we got:

$P(z$

b) between 7 and 12 months.

$P(7$

And we can find this probability with this difference:

$P(-2.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-2.5$

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1 year ago

In a study of crime, the FBI found that 13.2% of all Americans had been victims of crime during a 1-year period. This result was

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Answer: The lower bound of confidence interval would be 0.116.

Step-by-step explanation:

Since we have given that

p = 13.2%= 0.132

n = 1105

At 90% confidence,

z = 1.645

So, Margin of error would be

$z\sqrt{\dfrac{p(1-p)}{n}}\\\\=1.645\times \sqrt{\dfrac{0.132\times 0.868}{1152}}}\\\\=0.0164$

So, the lower bound of the confidence interval would be

$p-\text{margin of error}\\\\=0.132-0.0164\\\\=0.116$

Hence, the lower bound of confidence interval would be 0.116.

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1 year ago

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Answer:

B. $3927.54

Step-by-step explanation:

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2 years ago