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
Shkiper50 [21]
3 years ago
5

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 iterval (a, b) such that P{a≤Y≤b} ≥ 0.90b. 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:
strojnjashka [21]3 years ago
5 0

Answer:

a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

a= μ-3.16*σ , b= μ+3.16*σ

b) P(Y≥ μ+3*σ ) ≥ 0.90

b= μ+3*σ

Step-by-step explanation:

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

You might be interested in
Two legs of a right triangle are 4cm, and 3cm. find the length of the hypotenuse of this triangle
sergiy2304 [10]
It'll be 4^2+ 3^2 then the answer you get you take the square root of it which will give you the hypotenuse.
Your answer would be 5 because square root of 25 is 5
If u want the formula it's a^2+b^=c^2
C is the hypotenuse and a and b is the lengths
6 0
3 years ago
5y + 2 + 6 + 2y 5y + 2(y + 3) + 2 combining like terms 6y − y + 2y + 10 − 4 + 2 Commutative Property Distributive Property arrow
Paraphin [41]

Answer:

Distributive Property

Step-by-step explanation:

5y + 2 + 6 + 2y

= 5y + 2(y + 3) + 2 This is the distributive property of multiplication w.r.t. addition

= 6y − y + 2y + 10 − 4 + 2

The distributive property of multiplication with respect to addition  is the one  which separates each term by using multiplication and then addition.

So we see that 2 is multiplied with y and 3 and then added with the like terms. If there was a minus sign the property would be distributive over subtraction.

4 0
3 years ago
Solve for z: 11=6|-2z| -5
skad [1K]

Answer:

the roots are {-4/3, 4/3}

Step-by-step explanation:

Begin the solution of 11=6|-2z| -5 by adding 5 to both sides:

11=6|-2z| -5 becomes 16 = 6|-2z|.

Dividing both sides by 12 yields

16/12 = |-z|

There are two cases here:  first, that one in which z is positive and second the one in which z is negative.

If z is positive, 4/3 = -z, and so z = -4/3, and:

If z is negative, 4/3 = z

Thus the roots are {-4/3, 4/3}

3 0
3 years ago
The area of a rectangle with 2 1/2 as the width and 10 feet as the length
Tanya [424]
The formula for the area of a rectangle is:
A=wl
w = width
l = length

First, we have to convert 2 \frac{1}{2} into an improper fraction, then into a number. The improper fraction would be \frac{5}{2}. Let's convert that into a decimal.
5/2=2.5

Let's multiply
2.5*10=25
The area of the rectangle would be 25 feet!
7 0
3 years ago
I WILL MARK U BRAINLIEST PLEASEEE HELP ME WITH THIS!!!
slamgirl [31]

Answer:

this is answer

Step-by-step explanation:

Right now I don't have time. If u have doubt, send me a message. And I'll explain later.

hope it helps ☺️

6 0
3 years ago
Other questions:
  • A box can hold 4 books how many books can 5 boxes hold
    11·2 answers
  • I need to know the answer.
    7·1 answer
  • The volume of this cylinder is 6,430.72 cubic centimeters, the height is 8 cubic centimeters. What is the radius? Use ​ ≈ 3.14 a
    6·2 answers
  • Hayley borrowed $1,854 from her parents. She agreed to repay them in equal installments throughout the next 18 months. How much
    13·1 answer
  • Jason rolls a fair number cube labeled 1 through 6 and then he flips a coin what is the probability that he rolls a 3 and flips
    10·1 answer
  • What is the vertex of the function f(x) = x2 + 12x?
    13·2 answers
  • What is the Range of the function
    12·1 answer
  • Simplify the expression:<br> 10s+–2s
    6·2 answers
  • Which postulate (if any) should be used to show the triangles are congruent?
    11·1 answer
  • What is the equation of a line with slope -3 through the point (3, 5)?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!