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3 years ago

Let x have a poisson distribution with a variance of 3. find p(x = 2).

1 answer:

7 0

Since the variance of a Poisson distribution with rate parameter $\lambda$ is $\lambda^2$ , we know that $\lambda=\sqrt3$ . So,

$\mathbb P(X=2)=\dfrac{e^{-\sqrt3}(\sqrt3)^2}{2!}=\dfrac3{2e^{\sqrt3}}\approx0.2654$

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True or false please help it’s due right now

Free_Kalibri [48]

Answer:

false

Step-by-step explanation:

Triangle = 5*6=30/2=15

Parallelogram = 6*5 = 30

7 0

3 years ago

Read 2 more answers

Evaluate.

const2013 [10]

9514 1404 393

Answer:

-1/6

Step-by-step explanation:

A suitable calculator can evaluate this for you and show you the result as a fraction.

You start with the multiplication in the inner-most set of brackets. Here, those brackets are the absolute value function.

-2(-1/3) = +2/3

Then the sum in those brackets:

-5/6 +2/3 = -5/6 +4/6 = -1/6

The absolute value changes the sign of this back to positive, so the value in square brackets is ...

3 -(1/6) = 18/6 -1/6 = 17/6

Finally, this value is divided by -17, so you have ...

$\dfrac{17}{6}\div(-17)=\dfrac{17}{6}\cdot\dfrac{-1}{17}=-\dfrac{17\cdot1}{17\cdot6}=\boxed{-\dfrac{1}{6}}$

6 0

3 years ago

A student has learned that test scores in math are determined by this quadratic function: s(t) = -(t-6)^2 + 99

ser-zykov [4K]

Answer:

a. 6, b. 99, c. 63

Step-by-step explanation:

A) The function s(t) is in the vertex form. The standard vertex form is a(x-h)+k where the vertex is (h,k). The vertex is the highest (or lowest in some cases) point of the graph, so if we use s(t) to get the vertex we get that h=6 and k=99. This means that for a student to get a perfect score they need to study 6 hours

B) We can just take the k value from the first question because that's the highest value for s(t), so the highest score will be 99

C) For this one just plug in 0 for time, so -(0-6)^2+99. This equals -(-6)^2+99, which equals 99-36 =63

4 0

3 years ago

The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

b) $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

4 0

3 years ago

The new Coat and Jacket Store was ready to open. The workers put out 42 racks of men’s and boy’s coats and jackets with 16 items

Nataliya [291]

42 x 16=672
35 x 24=840

672+840=1512

3 0

3 years ago