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
quester [9]
2 years ago
7

100 POINTS!! How many relative extrema does the does the graph of the quartic function y = x^4– 3x^3 + x^2 + 2x – 1 have?

Mathematics
1 answer:
Marina CMI [18]2 years ago
4 0

Answer:

Hope this helps:)

Step-by-step explanation:

You might be interested in
What is the ratio of 18-29
ANEK [815]
62.069% is what i thank it is
6 0
3 years ago
Let X1 and X2 be independent random variables with mean μand variance σ².
My name is Ann [436]

Answer:

a) E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu

So then we conclude that \hat \theta_1 is an unbiased estimator of \mu

E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu

So then we conclude that \hat \theta_2 is an unbiased estimator of \mu

b) Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}

Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}

Step-by-step explanation:

For this case we know that we have two random variables:

X_1 , X_2 both with mean \mu = \mu and variance \sigma^2

And we define the following estimators:

\hat \theta_1 = \frac{X_1 + X_2}{2}

\hat \theta_2 = \frac{X_1 + 3X_2}{4}

Part a

In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:

E(\hat \theta_i) = \mu , i = 1,2

So let's find the expected values for each estimator:

E(\hat \theta_1) = E(\frac{X_1 +X_2}{2})

Using properties of expected value we have this:

E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu

So then we conclude that \hat \theta_1 is an unbiased estimator of \mu

For the second estimator we have:

E(\hat \theta_2) = E(\frac{X_1 + 3X_2}{4})

Using properties of expected value we have this:

E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu

So then we conclude that \hat \theta_2 is an unbiased estimator of \mu

Part b

For the variance we need to remember this property: If a is a constant and X a random variable then:

Var(aX) = a^2 Var(X)

For the first estimator we have:

Var(\hat \theta_1) = Var(\frac{X_1 +X_2}{2})

Var(\hat \theta_1) =\frac{1}{4} Var(X_1 +X_2)=\frac{1}{4} [Var(X_1) + Var(X_2) + 2 Cov (X_1 , X_2)]

Since both random variables are independent we know that Cov(X_1, X_2 ) = 0 so then we have:

Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}

For the second estimator we have:

Var(\hat \theta_2) = Var(\frac{X_1 +3X_2}{4})

Var(\hat \theta_2) =\frac{1}{16} Var(X_1 +3X_2)=\frac{1}{4} [Var(X_1) + Var(3X_2) + 2 Cov (X_1 , 3X_2)]

Since both random variables are independent we know that Cov(X_1, X_2 ) = 0 so then we have:

Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}

7 0
3 years ago
It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calcula
frosja888 [35]
The correct answer is true ~ Apex 
3 0
3 years ago
Read 2 more answers
khan academy 0.03 watts (W) per meter (m) per degree Celsius ( ∘ C). What is the batting's thermal conductivity value in cm⋅ ∘ C
solmaris [256]

#127373747299183747744

8 0
2 years ago
How do you solve linear systems
cluponka [151]

Answer:

Using various of methods. It depends of your solving it on a graph, table, etc.

Step-by-step explanation:

You can put it in slope-intercept form (My fav), standard form, point-slope form, you can find the rate change (Y is over X), etc.

8 0
3 years ago
Other questions:
  • He has a total of $45 to buy t tickets, each tickets cost $5
    9·1 answer
  • Model of how to find quotient 2.4 divided by 3
    15·1 answer
  • I don't know how to do this.
    13·1 answer
  • Choose all the numbers that are part of Integers.
    11·1 answer
  • If 120 marks is 60% what is full marks
    14·2 answers
  • A bag contains 2 red marbles , 3 green marbles , and 4 blue marbles.
    7·2 answers
  • If x does not equal 16 then 2x+10 does not equal 42​
    7·2 answers
  • HELP I NEED HELP ASAP!!
    10·2 answers
  • A jar contains 7 blue marbles and 2 red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you choose
    6·1 answer
  • A shape is rotated counterclockwise 110 degrees about the origin. What is another way to describe the rotation?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!