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3 years ago

What is the significance of the mean of a probability distribution?

Mathematics

1 answer:

VikaD [51]3 years ago

4 0

Answer:

Significance of the mean of a probability distribution.

Step-by-step explanation:

The mean of a probability distribution is the arithmetic average value of a random variable having that distribution.

For a discrete probability distribution, the mean is given by, $\sum x_iP(x_i)$ , where P(x) is the probabiliy mass function.
For a continuous probability distribution, the mean s given by, $E(x) = \int x_if(x_i)$ , where f(x) is the probability density function.
Mean is a measure of central location of a random variable.
It is the weighted average of the values that X can take, with weights given by the probability density function.
The mean is known as expected value or expectation of X.
An important consequence of this is that the mean of any symmetric random variable (continuous or discrete) is always on the axis of symmetry of the distribution.
For a continuous random variable, the mean is always on the axis of symmetry of the probability density function.

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Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be

Travka [436]

Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

dA/dt = in flow - out flow

Since litter falls at a constant rate of L grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

1/k∫-kdA/(L - Ak) = ∫dt

1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C' (C' = kC)

taking exponents of both sides, we have

$L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt} (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k} - \frac{C"}{k} e^{kt}$

When t = 0, A(0) = 0 (since the forest floor is initially clear)

$A = \frac{L}{k} - \frac{C"}{k} e^{kt}\\0 = \frac{L}{k} - \frac{C"}{k} e^{k0}\\0 = \frac{L}{k} - \frac{C"}{k} e^{0}\\\frac{L}{k} = \frac{C"}{k} \\C" = L$

$A = \frac{L}{k} - \frac{L}{k} e^{kt}$

So, D = R - A =

$D = \frac{L}{k} - \frac{L}{k} - \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{kt}$

when t = 0(at initial time), the initial value of D =

$D = \frac{L}{k} e^{kt}\\D = \frac{L}{k} e^{k0}\\D = \frac{L}{k} e^{0}\\D = \frac{L}{k}$

4 0

3 years ago

Really need help Pls

Studentka2010 [4]

Answer:

20.57 cm

Step-by-step explanation:

Circumference of half circle = diameter + half of circumference

$= 8 +\dfrac{2\pi r}{2}\\\\\\= 8 + \pi r\\\\= 8 + 3.142 * 4\\\\= 8 + 12.568\\\\= 20.568\\\\= 20.57 \ cm$

6 0

2 years ago

The Petri dish shown has no lid. What is the surface area of the outside of the Petri dish? Round to the nearest tenth. A cylind

Bess [88]

Answer:

12566.4 mm²

Step-by-step explanation:

The Petri dish shown has no lid. What is the surface area of the outside of the Petri dish? Round to the nearest tenth. A cylindrical-shaped Petri dish with a radius of 50 millimeters and a height of 15 millimeters.

TSA = Total Surface Area

CSA = Curved Surface Area

TSA of open cylinder = CSA of cylinder + area of base or top

= 2πrh + πr²

= πr(2h + r)

From the above question:

r = 50mm

h = 15mm

Hence,

= π × 50 (2 × 15 + 50)

= π × 50 (30 + 50)

= π × 50(80)

= π × 4000

= 12566.370614mm²

Approximately = 12566.4 mm²

The Surface Area of the petri dish with no lid = 12566.4 mm²

3 0

3 years ago

Out of 300 animals in the zoo 45 are birds what percent are not birds

Leya [2.2K]

Answer:

85%

Step-by-step explanation:

There are two ways to solve this.

1. You can find the percent of birds, and then subtract that from 100%.

To find the percent of birds, divide 45/300 or make the denominator 100 by dividing both parts by 3.

45/300 (as a fraction)

=15/100

That is the same as 15%.

Subtract that from 100% and you get 85%.

2. You find the number of non-bird animals and make that a percent.

300-45=255 non-bird animals

255/300 (as a fraction)

=85/100

That is the same as 85%.

So either way, the answer is 85%.

8 0

3 years ago

I really need help!

deff fn [24]

D=√(6-0)²+(2-10)²
d=√(6)²+(-8)²
d=√36+64
d=√100
d=10

6 0

3 years ago

What is the significance of the mean of a probability​ distribution?

What is the significance of the mean of a probability distribution?