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1 year 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]1 year 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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Answer:

a) 20 ways

b) 10 ways

Step-by-step explanation:

When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.

Part a)

We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2

General formula of permutations of n objects taken r at time is:

$nPr=\frac{n!}{(n-r)!}$

Using the value of n=5 and r=2, we get:

$5P2=\frac{5!}{(5-2)!} =20$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.

Part b)

Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.

The general formula of combinations of n objects taken r at a time is:

$nCr=\frac{n!}{r!(n-r)!}$

Using the value of n=5 and r=2, we get:

$5C2=\frac{5!}{2!(5-2)!} =10$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.

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If Line segment C B. bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three option

meriva

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Option (1)

Step-by-step explanation:

In the figure attached,

BC is the angle bisector of angle ACD.

To prove ΔABC and ΔDBC congruent by SAS property we require two sides and the angle between these sides to be congruent.

Since BC ≅ BC [Reflexive property]

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Therefore, Option (1) will be the answer.

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At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per

Vesna [10]

Answer:

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is

y = .07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down .03 per month, x. The equation for that is

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Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month. Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

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Now back sub in what x equals to solve for y. If x = 35, then in the first equation,

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y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.

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