A random variable x that assumes the values x1, x2, . . . , xk is called a discrete uniform random variable if its probability mass function is f(x) = 1 k for all of x1, x2, . . . , xk and 0 otherwise. find the mean and variance of x.
A discrete uniform random variable has values which are equally likely to occur. The mean can be calculated by summing all the values of the variable and dividing by the number of values, represented as μ = Σx/k. The variance, a measure of dispersion, can be calculated using the formula σ² = Σ(x − μ)²/k.
Explanation:In the context of a discrete uniform random variable, the mean (μ) and variance (σ²) can be calculated using specific formulas. This is related to the nature of a discrete uniform distribution, where x assumes the values x1, x2, ..., xk, and the probability of each outcome is equally likely.
Firstly, to find the mean
you simply need to add up all the values of x and divide by the number of values (k). This could be represented as μ = Σx/k.
Secondly, the variance can be calculated using the formula σ² = Σ(x − μ)²/k. In this equation, x represents the values of the random variable, μ is the mean (which we calculated earlier), and k represents the total number of values.
The concept here is essentially determining the central tendency (mean) and dispersion (variance) of a discrete uniform random variable. This is a fundamental topic in the field of probability and statistics.
Learn more about Discrete Uniform Distribution here:https://brainly.com/question/31603031
#SPJ3
A full bag of dog food weighs 5 1 2 pounds. How much dog food do you have if there are 3 3 4 bags in the cupboard
The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds
What are proper and improper fractions and how to convert mixed fractions to simple fractions?A fraction represents a part of a number or any number of equal parts.
There is a fraction, containing a numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called a proper fraction, otherwise, it is called an improper fraction. A proper fraction is also called a fraction that is less than 1. And an improper fraction is ≥ 1. A mixed fraction contains a sum of whole numbers and a proper fraction.
We have been given that a full bag of dog food weighs [tex]5\dfrac{1}{2}[/tex] pounds.
First, we need to convert mixed fractions into simple fractions;
[tex]5\dfrac{1}{2}[/tex] = 11/2
Also, [tex]3\dfrac{3}{4}[/tex] = 15/4
Therefore, we know there are 3 and 3/4 bags in the cupboard, and each one of them weighs 5 and 1/2 lbs, thus the total amount in the cupboard is just their product.
[tex]5\dfrac{1}{2}[/tex] × [tex]3\dfrac{3}{4}[/tex]
11/2 × 15/4
= [tex]20\dfrac{5}{8}[/tex]
Hence, The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds.
Learn more about fractions;
https://brainly.com/question/729654
#SPJ2
A box contains 13 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective.
b. none are defective.
Answer:
A. 1/1287
B. 56/1287
Step-by-step explanation:
Probability of getting all are defective transistors is 5/12.
Given that, a box contains 13 transistors, 5 of which are defective.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
a) Probability of getting all are defective
Number of favorable outcomes = 5
Total number of outcomes = 12
Probability of getting all are defective = 5/12
b) Probability of getting none are defective
Number of favorable outcomes = 7
Total number of outcomes = 12
Probability of getting none are defective = 7/12
Therefore, probability of getting all are defective transistors is 5/12.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ5
Rami sold concessions during a concert. He sold bottled water for $3.50 each and bags of trail mix for $4 each. By the end of the evening, Rami sold 400 items for a total of $1,475. How many bottles of water and how many bags of trail mix did Rami sell?
Rami sold 250 bottles of water and 150 bags of trail mix at the concert, totaling $1,475 in sales.
To solve the problem of how many bottles of water and bags of trail mix Rami sold, we need to set up and solve a system of linear equations based on the given information.
Let's define the variables:
- [tex]\( x \)[/tex] = the number of bottles of water sold
- [tex]\( y \)[/tex] = the number of bags of trail mix sold
From the problem, we have two pieces of information that we can turn into equations:
1. The total number of items sold is 400.
2. The total revenue from the items sold is $1,475.
We can write these two statements as equations:
1. [tex]\( x + y = 400 \)[/tex]
2. [tex]\( 3.50x + 4y = 1475 \)[/tex]
We now have a system of linear equations:
[tex]\[\begin{cases}x + y = 400 \\3.50x + 4y = 1475\end{cases}\][/tex]
Step 1: Solve the first equation for [tex]\( y \)[/tex]
[tex]\[y = 400 - x\][/tex]
Step 2: Substitute [tex]\( y \)[/tex] in the second equation
Replace [tex]\( y \)[/tex] in the second equation with [tex]\( 400 - x \)[/tex]:
[tex]\[3.50x + 4(400 - x) = 1475\][/tex]
Step 3: Simplify and solve for [tex]\( x \)[/tex]
Expand and simplify the equation:
[tex]\[3.50x + 1600 - 4x = 1475\][/tex]
Combine like terms:
[tex]\[3.50x - 4x + 1600 = 1475\][/tex]
[tex]\[-0.50x + 1600 = 1475\][/tex]
Subtract 1600 from both sides:
[tex]\[-0.50x = 1475 - 1600\][/tex]
[tex]\[-0.50x = -125\][/tex]
Divide both sides by -0.50:
[tex]\[x = \frac{-125}{-0.50} = 250\][/tex]
So, Rami sold 250 bottles of water.
Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]
Substitute [tex]\( x = 250 \)[/tex] back into the first equation:
[tex]\[y = 400 - 250 = 150\][/tex]
So, Rami sold 150 bags of trail mix.
Conclusion
Rami sold:
- 250 bottles of water
- 150 bags of trail mix
To verify, we check the total revenue:
[tex]\[3.50 \times 250 + 4 \times 150 = 875 + 600 = 1475\][/tex]
The numbers match the given total revenue, confirming our solution is correct.
A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign? $$
Answer:
2916/289 = 10 26/289 ≈ 10.09
Step-by-step explanation:
The ratio of areas of similar figures is the square of the scale factor. Here, the scale factor is the ratio of lengths, so is ...
k = banner/sign = 54/17
The ratio of areas is k² = (54/17)² = 2916/289 = 10 26/289 ≈ 10.09
The ratio of the area of the school banner to the area of the sign is approximately 3.36:1. This was calculated by first finding the areas of both the banner and the sign, and then dividing the area of the banner by the area of the sign.
Explanation:The subject of this question falls under Mathematics, and it deals with the concept of ratio and similar figures. In this case, the figures are a school banner and a sign, both of which are rectangular in shape. The ratio of their areas can be determined by calculating the areas of both figures and then finding the ratio of the two values.
Firstly, let's calculate the area of the school banner. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the school banner = 54 inches (length) * 36 inches (width) = 1944 square inches.
Next, the sign's width isn't given, but because the two shapes are similar, the ratio of the banner's length to its width is equal to the ratio of the sign's length to its width. So, if we let 'w' be the width of the sign, then 54/36 = 17/w. Solving this for 'w', the width of the sign = [tex](17 * 36) / 54 = 17*2 = 34[/tex] inches. The area of the sign, then, is 17 inches (length) * 34 inches (width) = 578 square inches.
To get the ratio of the school banner's area to the sign's area, divide 1944 by 578, which equals approximately 3.36. Therefore, the ratio of the areas is 3.36:1. Meaning for every square inch of the sign, there are approximately 3.36 square inches of the school banner.
Learn more about Ratio and Proportions here:https://brainly.com/question/26974513
#SPJ11
Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take rich and Michelle to meet?
Answer:
2 7/27 hours, about 2 hours 15 minutes, 33 seconds
Step-by-step explanation:
You want to know how long it takes for Rich and Michelle to meet if they start 305 miles apart and are driving toward each other. Rich is driving 70 mph, and Michelle is driving 65 mph.
Closing speedThe speed at which they are moving toward each other is ...
70 mph + 65 mph = 135 mph
Meeting timeThat means they will reduce their separation distance to zero after ...
time = distance / speed
time = (305 mi)/(135 mi/h) = 2 7/27 h
It will take 2 7/27 hours, about 2.26 hours, for Rich and Michelle to meet.
<95141404393>
is this correct....help me with the 2 questions
There are 18 students enrolled in Mr. Baker's class. Today 3 of them are absent. What is the ratio of the number of students present in class today to the total number enrolled?
Answer:
5/6
Step-by-step explanation:18 total -3 absent = 15
15 divided by 3
18 divided by 3=
5/6
The ratio for the given two numbers is 5 : 6.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The total number of students are given as 18.
And, the number of students absent is 3.
Then, the number of present students is given as 18 - 3 = 15.
Now, the ratio as per the given case can be obtained as follows,
Number of students present ÷ Number of enrolled students
⇒ 15 ÷ 18
⇒ 15/18
⇒ 5 : 6
Hence, the required ratio for the two numbers is 5 : 6.
To know more about ratio and proportion click on,
brainly.com/question/14279414
#SPJ2
Two sides of a triangle are equal in length, and the third side is 5 inches. If the perimeter is 17 inches, how long are the two equal sides?
Zach has 53 flowers to plant. he wants to plant them in groups of 10s and 1s. zach can plant 10 flowers in each flower box. He can plant 1 flower in each pot. Zach only wants to plant a group of ten flowers in each box. Is there any way that zach could plant all 53 flowers using boxes only? Explain your answer.
Solution:
we are given that
Zach has 53 flowers to plant.
He wants to plant them in groups of 10s and 1s.
zach can plant 10 flowers in each flower box.
Zach only wants to plant a group of ten flowers in each box.
We have been asked to find Is there any way that zach could plant all 53 flowers using boxes only?
since zach can plant 10 flowers in each flower box. so in 5 boxes he can plant
50 flowers.
Now we have 3 left. These 3 can be planted in pot.
But he wants to use boxes only with 10 flowers in each box.
So its not possible to plant all 53 flowers using boxes only.
ABCD and JKLM are similar rectangles. What is the perimeter of JKLM?
21 m
22 m
24 m
28 m
Answer:
Step-by-step explanation:
21
Find the equation of the line that has these features: slope, m=-6/5 passes through the point (-5,10)
Read the line of poetry:
And the dish ran away with the spoon.
This line is an example of what term?
A.
alliteration
B.
personification
C.
onomatopoeia
D.
imagery
Please help I AM SO SCARED IF I FAIL THIS...
The enrollment in college A may be modeled by y = 0.046x + 0.570, and the enrollment in college B may be modeled by y = –0.036x + 2.702, where x is the number of years since 1990 and y is the enrollment in thousands. When will the two colleges have the same enrollment and what is that enrollment?
In 1974, both colleges had an enrollment of 1,766 students.
In 2016, both colleges will have an enrollment of 1,766 students.
In 2012, both colleges will have an enrollment of 1,122 students.
In 1992, both colleges had an enrollment of 1,600 students.
Answer:
In 2016, both colleges will have an enrollment of 1,766 students.
Step-by-step explanation:
gradpoint
PLZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPP!
Using similarity solve for x. Show all work.
The enrollment in college a may be modeled by y = 0.051x + 0.470, and the enrollment in college b may be modeled by y = –0.041x + 1.850, where x is the number of years since 1990 and y is the enrollment in thousands. when will the two colleges have the same enrollment and what is that enrollment?
In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.
What is Two Variable linear Equation?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Here, given relation between enrollment year and total number of enrollment
y = 0.051x + 0.470 ..............(i)
y = -0.041x + 1.850 ................(ii)
On comapring eq. (i) and eq. (ii), we get
0.051x + 0.470 = -0.041x + 1.850
0.051x + 0.041x = 1.850 - 0.470
0.092x = 1.380
x = 1.380 / 0.092
x = 15
put the value of x in equation (i), we get
y = 1235
Thus, In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.
Learn more about Two variable equation from:
https://brainly.com/question/24085666
#SPJ2
someone help me on this question please
Express the confidence interval (0.070, 0.126) in the form of
A particle moves along the x-axis in such a way that its velocity at any time t > 0 is given by v(t)=3t^2-4t-4. the particl's position x(t) has a value of 1 when t=1
bob started mowing at 9:55 am .It took him 25 minutes to mow the front yard and 45 minutes to mow back yard.at what did bob finish mowing?
Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? Enter your answer in the box
https://static.k12.com/nextgen_media/assets/8120449-SUM_CR_GMT_SemB_06_UC_DP100_864_003.jpg
The table below shows the total cost for purchasing a certain number of equally-priced concert tickets. Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),
Answer:
c = 55t
Step-by-step explanation:
Since there are no handling fees and the price of tickets is constant, we know the cost will be proportional to the number of tickets purchased. The generic form of an equation expressing a proportional relationship between cost (c) and number of tickets (t) is ...
c = kt
where k is the constant of proportionality (the cost per ticket). We can find k by using any of the data points given in the table. Using the first point, we have ...
110 = k·2
110/2 = k = 55 . . . . . divide by 2
Then using this value for k, the desired equation can be written ...
c = 55t
If r = 1, s = 2, and t = 3, what value do you expect y will have?
When changes in one variable are usually accompanied by changes in the same direction in another variable?
a small bunch of flowers costs $5 and a large bunch costs $20. what fraction of the cost of the large bunch is the small bunch
I Need help please cmon
The angle a vector makes with the x-axis of a coordinate system must be what size in order to make one or more of its components negative? A) Less the 30 degrees B) between 30 and 60 degrees C) between 61 and 90 degrees D) greater then 90 degrees
Answer:
Greater than 90 degrees.
Step-by-step explanation:
Let a vector R make angle [tex]\theta[/tex] with the x-axis. Then, the component along the x-axis would be
[tex]R cos\theta[/tex]
Component along y-axis would be
[tex]R sin\theta[/tex]
For [tex]0<\theta<90[/tex] both the components will be positive and lie in the first quadrant. If angle of vector is more than 90 degrees, one of the components would be negative. For example, angle between 90 to 180 degrees, x-component would be negative while between 180-270 degrees, both the components would be negative.
Which of the following graphs matches the circle defined by this equation ? (X+2)^2+(y-4)^2=9
This equation represents the circle having a radius of 3 units and a center situated at (-2, 4). Hence, graph D is correct.
Use the concept of a circle defined as:
A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.
A circle is also known as the location of points that are evenly spaced apart from the center.
The radius of a circle is measured from the center to the edge.
The given equation of a circle is:
(X+2)²+(y-4)²= 9
Since we know that,
The general equation of the circle is,
(x-a)²+(y-b)²= r²
Where (a, b) is the center of the circle
r is the radius of the circle.
Now compare with the given equation we have,
(a, b) = (-2, 4)
And radius r² = 9
Then r = 3
Then this circle has a radius of 3 units and a center situated at (-2, 4).
Hence,
Graph D is correct.
To learn more about Circle visit:
https://brainly.com/question/29288238
#SPJ4
The complete question is:
Which of the following graphs matches the circle defined by this equation? (x-a)²+(y-b)²= r²
2, 3, 6, 8, . . . is an example of an infinite alternating series. True False
Answer:
false
Step-by-step explanation:
took the test
Why is partitioning a directed line segment with a ratio of 1:2 not the same as finding half the length of the directed line segment
Answer:
Sample response: A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.
Step-by-step explanation: