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
Ne4ueva [31]
2 years ago
13

Please help me with the question

Mathematics
1 answer:
mars1129 [50]2 years ago
3 0

(i) The mean is

\displaystyle E(X) = \sum_x x \, P(X = x) \\\\ E(X) = 1\cdot0.175 + 2\cdot0.315 + 3\cdot0.211 + 4\cdot0.092 + 5\cdot0.207 \\\\ \boxed{E(X) = 2.839}

The variance is

V(X) = E((X - E(X))^2) = E(X^2) - E(X)^2

Compute the second moment E(X^2) :

\displaystyle E(X^2) = \sum_x x^2 \, P(X = x) \\\\ E(X) = 1^2\cdot0.175 + 2^2\cdot0.315 + 3^2\times0.211 + 4^2\times0.092 + 5^2\times0.207 \\\\ E(X^2) = 9.997

Then the variance is

\boxed{V(X) \approx 1.9171}

(ii) For a random variable Z=aX+b, where a,b are constants, we have

E(Z) = E(aX+b) = E(aX) + E(b) = a E(X) + b

and

V(Z) = E((aX+b)^2) - E(aX+b)^2 \\\\ V(Z) = E(a^2 X^2 + 2ab X + b^2) - (a E(X) + b)^2 \\\\ V(Z) = a^2 (E(X^2) - E(X)^2) \\\\ V(Z) = a^2 V(X)

Then for Y=\frac{X+3}2, we have

E(Y) = \dfrac12 E(X) + \dfrac32 \\\\ \boxed{E(Y) = 2.918}

E(Y^2) = E\left(\left(\dfrac{X+3}2\right)^2\right) = \dfrac14 E(X^2) + \dfrac32 E(X) + \dfrac94 \\\\ \boxed{E(Y^2) \approx 9.0028}

You might be interested in
At the neighborhood block party, Camille served 1/2 of a gallon of hot chocolate and 1/3 of a gallon of apple cider. How much mo
Oksi-84 [34.3K]

Answer:

1/6 more hot chocolate than apple cider.

Step-by-step explanation:

In order to complete this, you first have to make both numbers have the same denominator.

2: 2, 4, 6

3: 3, 6

<em>The </em><em>new </em><em>denominator </em><em>is </em><em>6</em><em>.</em>

1/2 - 3/6

1/3 - 2/6

These are the new fractions after making the numbers have common denominators.

3/6 - 2/6 = 1/6

Camille serves <em>1</em><em>/</em><em>6</em><em> </em>more hot chocolate than apple cider.

7 0
3 years ago
How many rice balls can Justin make with 700700700 grams of rice?
user100 [1]

Answer:

im pretty sure its 777 hope this helped:)

4 0
3 years ago
What is the completely factored form of x3 – 64x?
Arada [10]

Answer:

x( x-8)(x+8)

Step-by-step explanation:

x^3 - 64x

Factor out an x

x( x^2 -64)

This is the difference of squares x^2 -8^2 which is a^2 - b^2 = (a-b)(a+b)

x( x-8)(x+8)

4 0
3 years ago
Read 2 more answers
HELP DUE TOMORROW ANSWER ALL FOUR PARTS PLZ
NikAS [45]

Answer:

7. A

8. C

9. C

10. A

Step-by-step explanation:

You just have to work each one out. This is very simple.

6 0
3 years ago
PLEASE ANSWER FAST
Nadya [2.5K]
A. The scatter plot has an outlier at (4, 11).
 Remember that the ordered pair is of the form:
 (x, y).
 That is, the first value represents the axis of the x.
 The second value represents the y-axis.
 The scatter plot has an outlier at
 (x, y) = (4, 11)
 x = 4
 y = 11
 C.The scatter plot has a cluster with a domain from 10 to 12.
 
Remember that when we speak of domain we refer to the values of x in the function.
 Therefore in domain 10 <= x <= 12 The scatter plot has a cluster
6 0
3 years ago
Other questions:
  • Identify the molecule that is a carbohydrate.
    10·2 answers
  • Problem Page A bucket holds 50.7 ounces of water. How much is this in liters? Use the following conversion: 1 liter is 33.8 ounc
    8·1 answer
  • Someone explain why 1+1=2 in simple terms
    14·1 answer
  • In a math class of 32 students, 18 boys and 14 are girls. On a unit test, 5 boys and 7 girls made an A grade. A student is chose
    13·1 answer
  • A culture of bacterial triples in size every four hours. If the bacteria population is estimated to be three million now, what w
    15·2 answers
  • Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 900
    13·1 answer
  • 2.<br> Given points A(3, -5) and B(19,-1), find the coordinates of point C such that he =
    7·1 answer
  • Is (-2,-6) a solution of y &lt; 7x + 8?​
    11·2 answers
  • Solve each equation. Show your work please. Part 2​
    11·1 answer
  • Help on this question pls
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!