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3 years ago

A uniform distribution is defined over the interval from 6 to 10.

Mathematics

1 answer:

zhuklara [117]3 years ago

8 0

Answer:

Refer below

Step-by-step explanation:

a) a and b are the lower and higher values of the interval for which uniform distribution is defined.

Here a= 6 and b =10

b) Mean of the uniform distribution= (a+b)/2 = (6+10)/2 =8

Or int x (1/4) dx = x^2/8 = 8

c) Variance of the uniform distribution = (b^2-a^2)/12 = (100-64)/12

= 36/12 =3

Std dev = sq rt of 3 = 1.732

d) To find total area

PDF of the distribution = 1/(b-a) = 1/4, 6<x<10

Area = \int 6 to 10 of 1/4 dx

= x/4

Subtitute limits

= (10-6)/4 =1

So total area = 1

d)P(X>7) = int 7 to 10 of 1/4 dx = 3/4

e) P(7<x<9) = Int 7 to 9 of 1/4 dx = 2/4 = 1/2

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In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that

attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let <em>X</em> = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...$

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7\times0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

6 0

3 years ago

The cost, c(x), for a taxi ride

viva [34]

Answer:

The answer is A.

Go to desmos and type your equation in

3 0

3 years ago

Can some explain steps

Mashutka [201]

Answer:

r = 3.

Step-by-step explanation:

16 = 10 + √(3r + 27)

√(3r + 27) = 6

Square both sides:

3r + 27 = 36

3r = 36 - 27 = 9

r = 3.

Check the result:

Left side of the equation = 16

Right side = 10 + √(9 + 27)

= 10 + √36 = 16

5 0

2 years ago

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What is the rate of change for this imagine

GaryK [48]

3, -1

Step-by-step explanation:

It goes 3 to the positive side

and one down side

4 0

3 years ago

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Two lines intersect at a point, forming ∠1 , ∠2 , ∠3 , and ∠4 .

Ad libitum [116K]

The answer is: [B]: " 60° " .
________________________________________
Because at whatever location, <span>∠2 and ∠4 are vertical angles;
</span>
and all vertical angles have equal measurements.

Given: m∠1 is 120°, and ∠1 is supplementary to ∠2 ;

then m∠1 + m∠2 = 180° .

So, m∠2 = (180 - 120)° = 60° .

As aforementioned:

m∠4 = m∠2 = 60° ; which is: Answer choice: [B]: " 60° " .
___________________________________________________

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3 years ago