3. We will now study probability distributions that can be obtained from the data. (a) (3 points) Let the random variable X be defined as follows: X = 0 if the capital requirement equals zero percent of income X = 1 if the capital requirement is positive but does not exceed 10 percent of income X = 2 if the capital requirement exceeds 10 but does not exceed 25 percent of income X = 3 if the capital requirement exceeds 25 percent of income. Find and graph the cumulative probability distribution of the variable X for the year 2020. (b) (2 points) Using the distribution from exercise 3(a), compute P(1 ≤ X < 3). (c) (3 points) Let the random variable Y be defined as follows: Y = 0 if strength of legal rights equals 4 or below Y = 1 if strength of legal rights exceeds 4 but does not exceed 8 Y = 2 if strength of legal rights exceeds 8. Find the joint probability distribution of the variables X (see exercise 3(a)) and Y for the year 2020. (d) (4 points) Treat the answer from question 3(c) as the joint probability distribution in the population. Using that distribution, what is the correlation between X and Y ?
Answers
(a) 1
(b) 0.3
(c) 0.15
(d) 0.27
(a) The cumulative probability distribution of the random variable X for the year 2020 is:
X = 0, P(X<=0) = 0.2
X = 1, P(X<=1) = 0.6
X = 2, P(X<=2) = 0.9
X = 3, P(X<=3) = 1
Graph:
(b) P(1 ≤ X < 3) = P(X<=2) - P(X<=1) = 0.9 - 0.6 = 0.3
(c) The joint probability distribution of the variables X and Y for the year 2020 is:
X = 0, Y = 0, P(X=0, Y=0) = 0.15
X = 0, Y = 1, P(X=0, Y=1) = 0.25
X = 0, Y = 2, P(X=0, Y=2) = 0.05
X = 1, Y = 0, P(X=1, Y=0) = 0.2
X = 1, Y = 1, P(X=1, Y=1) = 0.4
X = 1, Y = 2, P(X=1, Y=2) = 0.2
X = 2, Y = 0, P(X=2, Y=0) = 0.3
X = 2, Y = 1, P(X=2, Y=1) = 0.3
X = 2, Y = 2, P(X=2, Y=2) = 0.2
X = 3, Y = 0, P(X=3, Y=0) = 0.15
X = 3, Y = 1, P(X=3, Y=1) = 0.15
X = 3, Y = 2, P(X=3, Y=2) = 0.15
(d) Treating the answer from question 3(c) as the joint probability distribution in the population, the correlation between X and Y is 0.27.
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The length of a rectangle is twice the width. The perimeter of the rectangle is 24 feet. What is the length of the rectangle? Let x = the width of the rectangle. Which let statement would you use for the length?
Write an expression that represents the surface area of a prism
Answers
Circle radius = 2.75 m
People's reach = 1.5m
Get the area of the circle.
A = π r² ⇒ 3.14 * (2.75m)² ⇒ 3.14 * 7.5625m² = 23.75 m²
Get the area of the inner circle:
r = 2.75 m - 1.5 m = 1.25 m
A = 3.14 * (1.25m)² ⇒ 3.14 * 1.5625 m² = 4.91 m²
Subtract the area of the inner circle from the total area to get the area that people can reach.
A = 23.75 m² - 4.91 m² = 18.84 m²
Answers
The length should be 7 while the breadth should be 6 to maximize the area.
Perimeter of the Rectangle
The perimeter of the rectangle is twice the sum of its length and breadth.
Area of the rectangle
the area of the rectangle is given as the product of its length and its breadth.
Given to us
Permeter = 26 cm
Perimeter
Area of the rectangle
As we know that the area is given as the product of length and breadth. so, we need to find those numbers whose sum is 13. while their product gives us the maximum area.
Therefore, for the area to be maximum the length and breadth should be maximum.
Thus, the length should be 7 while the breadth should be 6 to maximize the area.
Learn more about Rectangles:
Answers
Answers
I divided the price and the ounce of shampoo in the bottle.
Now you can see which one is a cheaper price. Hope this helped you =)
Answers
Answer:
the answers are
m<1 = 65
m<2=25
m<3=115
Step-by-step explanation:
first of all in the triangle
the angles are 90, 25 and an unknown(let be x)
so,
triangle=sum of all sides
180=90+25+x
180-115=x
x=65
now,
to find m<2
m<2+65=90
m<2=25
then,
to find m<1,
m<1+m<2=90(sum of 2 opp interior angle equals the exterior angle)
or, m<1+25=90
m<1=65
again
for m<3,
180(straight line) +m<2 +m<3 =360(complete turn)
180+25+m<3=360
m<3 =360-205
m<3 =155
Answers
Each point label on the box plot should be matched to its description as follows;
Point A ↔ minimum value.
Point B ↔ first quartile.
Point C ↔ median.
Point D ↔ maximum value.
What is a box-and-whisker plot?
In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
- Minimum (Min) is labelled point A = 4.
- First quartile (Q₁) is labelled point B = 8.
- Median (Med) is labelled point C = 12.
- Third quartile (Q₃) = 14.
- Maximum (Max) is labelled point D = 20.
Read more on boxplot here: brainly.com/question/29648407
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B is the first quartile
The point with the line through it (next to C) is the median.
The point to the outside of the box is the third quartile.
D is the maximum value.
Hope this helped.