1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oksanka [162]
1 year ago
13

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

note the number of fish that need be caught to obtain at least one of each type.
(a) Give an interval (a, b) such that (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?
Mathematics
1 answer:
gregori [183]1 year ago
4 0

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

You might be interested in
the 8th grade class planned a trip to kings dominion and 120 students went. Ten students rode with their parents. The rest rode
Papessa [141]

120-10=110/2=55 students per bus

5 0
3 years ago
Read 2 more answers
Fill in the blank with a fraction to make a true statement: 1/3 + _____ = 1/2
HACTEHA [7]

Answer:

1/6

Step-by-step explanation:

1/3 + /1/6= 1/2

Because 1.5 is half of 3

5 0
2 years ago
PLEASE DO IT it is due in 5 minutes
german
A) 42x-12
6*7=42. 6*2=12
b) 21y
11+4+6=21
4 0
3 years ago
Read 2 more answers
Maya shaved her head and then began letting her hair grow. She represents the length L of her hair, in centimeters, m months aft
Lesechka [4]
Answer:

1.25 means that in one month, her hair will grow 1.25 centimeters.
3 0
3 years ago
Read 2 more answers
Can someone please help me with this question?
Alinara [238K]

Answer:

im pretty sure its a

Step-by-step explanation:

because the water level is pretty much the same even when theres more swimmers

4 0
2 years ago
Other questions:
  • What is 95/50 As a decimal
    14·1 answer
  • What is the ratio of 48 cans for $9.00
    13·2 answers
  • What is the domain and range of f(x)=2|x-4|
    10·1 answer
  • What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters?
    5·1 answer
  • Express 84,42 as a percentage of 74,05 rounded off to a whole number
    5·1 answer
  • Choose the statement that is true.
    10·1 answer
  • Help me with this!! I dont understand this question
    6·1 answer
  • Choose 3 values that would make thi inequalitie true 28+x&gt;42
    9·1 answer
  • A traveler is trying to determine the fastest way to travel from city A to city Z. The possible travel routes, with the time req
    12·1 answer
  • 8 people want to share a large pizza.Use a ratio to express how many pieces each person gets if the pizza is divided equally
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!