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
How do you do equations and equalities on a number line
castortr0y [4]
To graph an equation on a number line, You place a point at where the number lies. For example, x=5 would mean that you place a point on 5 and not draw a line.

To graph an inequality on a number line, if depends if it is <, >, ≤, or ≥ . If it is ≤, it is a closed point on the number and a line moving to the left of the number. If it is a ≥, then it is a closed point on the number with a continuous line to the right. If it is a <, it is an open point on the number with a line going to the left. If it is a >, then it is an open point going to the right.

I'll attach a photo to show you what it looks like! :) Hope this helps! :)

8 0
3 years ago
one vertex of a triangle is located at (0,5) on a coordinate grid after a transformation the vertex is located at(5,0) which tra
Alik [6]

Answer:

It's a rotation clockwise of 90 degrees about the origin.

Step-by-step explanation:

The given point moves from   y = 5 to x = 5 so it has passed through 90 degrees about the origin.

It's a rotation clockwise of 90 degrees about the origin.

6 0
3 years ago
1 6 36 216 what come next
baherus [9]
The answer will be 346
8 0
3 years ago
Read 2 more answers
HELP...here say:write five decimals that have at least 3 digits to the right of the decimal point.Write the expanded form and th
just olya [345]
27÷9=3
1+2=3
1×3=3
10-7=3
27-24=3
8 0
2 years ago
Type the correct answer in the box. Use a comma to separate the x- and y-coordinates of each point. The coordinates of the point
MAVERICK [17]

Answer:

On a unit circle, the point that corresponds to an angle of 0^{\circ} is at position (1, \, 0).

The point that corresponds to an angle of 90^{\circ} is at position (0, \, 1).

Step-by-step explanation:

On a cartesian plane, a unit circle is

  • a circle of radius 1,
  • centered at the origin (0, \, 0).

The circle crosses the x- and y-axis at four points:

  • (1, \, 0),
  • (0, \, 1),
  • (-1,\, 0), and
  • (0,\, -1).

Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.

When the angle is equal to 0^\circ, the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be (1, \, 0).

To locate the point with a 90^{\circ} angle, rotate the 0^\circ segment counter-clockwise by 90^{\circ}. The segment would land on the positive y-axis. In other words, the 90^{\circ}-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be (0, \, 1).

4 0
3 years ago
Other questions:
  • O'Connor breakfast foods produced 6,552 of crispy corn cereal. the company wants to put the cereal into boxs that hold 12 ounces
    8·1 answer
  • The volume of Jupiter is approximately 10^14 cubic kilometers. The volume of Earth is approximately 10^11 cubic kilometers. How
    10·1 answer
  • 3. Given: Circle Q<br>&lt;A = 35<br>Find: m AB​
    10·1 answer
  • 7ab=c solve for a. Answer
    7·1 answer
  • These box plots show daily low temperatures for a sample of days In two different towns
    13·2 answers
  • Doug and Elizabeth planted a garden on their farm. They wish to increase its dimensions by 50% without changing the shape of the
    15·1 answer
  • Please help.<br><br> For math class
    14·1 answer
  • What is the volume of the cylinder below?<br><br> Use 3.14 for pi.
    6·1 answer
  • Give inverse of each other relations <br><br><br> a. R={(x,y):is a brother or y}​
    6·1 answer
  • Can someone help me answer this
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!