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Ymorist [56]
3 years ago
9

The function f (x) = 4(3) can be used to determine the number of

Mathematics
1 answer:
kumpel [21]3 years ago
5 0
Your answer is: f(x)= 12
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A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y de
gregori [183]

a= μ-3.16*σ , b= μ+3.16*σ if each fish caught is equally likely to be any one of these 4 distinct types.

<h3>What is meant by Chebyshev inequality?</h3>

Chebyshev's inequality is a probability theory that ensures that, over a vast range of probability distributions, no more than a particular proportion of values would be present within a selected limits or range as from mean. In other words, only a certain fish caught will be discovered within a given range of the distribution's mean.

The formula for which no more than a particular number of values can exceed is 1/K2; in other words, 1/K2 of a distribution's values can be more than or equal to K standard deviations away from the distribution's mean. Furthermore, it asserts that 1-(1/K2) of a distribution's values must be within, but not include, K standard deviations of the distribution's mean.

How to solve?

from Chebyshev's inequality for Y

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

where

Y =  the number of fish that need be caught to obtain at least one of each type

μ = expected value of Y

σ = standard deviation of Y

P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean

k= parameter

thus for

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

P{a≤Y≤b} ≥ 0.90 →  1-1/k² = 0.90 → k = 3.16

then

P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

using one-sided Chebyshev inequality (Cantelli's inequality)

P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)

P{Y≥b} ≥ 0.90  →  1- σ²/(σ²+λ²)=  1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ

then for

P(Y≥ μ+3*σ ) ≥ 0.90

In order to learn more about Chebyshev inequality, visit:

brainly.com/question/24971067

#SPJ4

4 0
1 year ago
The graph below represents the average monthly rainfall (y), in inches, in
White raven [17]

Answer:

The amount of rainfall increases as an exponential function of time.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The angles of a triangle are 989, 51°, and x®,<br> What is the value of x?
Anastaziya [24]

9514 1404 393

Answer:

  x = 31

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  98° +51° +x° = 180°

  x° = 31° . . . . . . . . . . . . subtract 149°

  x = 31

6 0
2 years ago
N=3x45 write what n represents in the related division problem
Hitman42 [59]
One hundred thirty five 13%
6 0
3 years ago
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A game stop membership cost $20 and includes one game A month for five dollars. Nonmembers can get one more game a month for sev
miss Akunina [59]

Answer:

C(x) = 5x + 20 (for members)

C(x) = 3.5x (for non-members)

Step-by-step explanation:

Cost of membership = $20

Price of a game per month = $5

So, the linear equation to compute the total cost for a member can be computed by:

C(x) = 5x + 20

where x is the number of games per month

On the other hand, non-members can get one more game per month for $7 which means they get 2 games for $7. The price for a single game is $7/2 = $3.5 a month.

The linear equation to compute the total cost for a non-member is:

C(x) = 3.5x

where x is the number of games per month.

The following system of equations can be used to decide whether to become a member or not, by substituting the number of games in place of x and finding out the total cost.

C(x) = 5x + 20 (for members)

C(x) = 3.5x (for non-members)

3 0
3 years ago
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