Let X be the number of the cars being repaired at a repair shop. We have the following information:
At any time, there are at most 3 cars being repaired.
The probability of having 2 cars at the shop is the same as the probability of having one car.
The probability of having no car at the shop is the same as the probability of having 3 cars.
The probability of having 1 or 2 cars is half of the probability of having 0 or 3 cars.
(a) What is the sample space?
(b) Find the pmf of X and draw the histogram of pmf.
(c) Find the cdf of X and draw the histogram of cdf.
Answers
Answer:
(a) Sample Space
[tex]S = \{0,1,2,3\}[/tex]
(b) PMF
[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {P(x)} & {1/3} & {1/6} & {1/6} & {1/3} \ \end{array}[/tex]
(c) CDF
[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {F(x)} & {1/3} & {1/2} & {2/3} & {1} \ \end{array}[/tex]
Step-by-step explanation:
Solving (a): The sample space
From the question, we understand that at most 3 cars will be repaired.
This implies that, the number of cars will be 0, 1, 2 or 3
So, the sample space is:
[tex]S = \{0,1,2,3\}[/tex]
Solving (b): The PMF
From the question, we have:
[tex]P(2) = P(1)[/tex]
[tex]P(0) = P(3)[/tex]
[tex]P(1\ or\ 2) = 0.5 * P(0\ or\ 3)[/tex]
[tex]P(1\ or\ 2) = 0.5 * P(0\ or\ 3)[/tex] can be represented as:
[tex]P(1) + P(2) = 0.5[P(0) + P(3)][/tex]
Substitute [tex]P(2) = P(1)[/tex] and [tex]P(0) = P(3)[/tex]
[tex]P(1) + P(1) = 0.5[P(0) + P(0)][/tex]
[tex]2P(1) = 0.5[2P(0)][/tex]
[tex]2P(1) = P(0)[/tex]
[tex]P(0)= 2P(1)[/tex]
Also note that:
[tex]P(0) + P(1) + P(2) + P(3) = 1[/tex]
Substitute [tex]P(2) = P(1)[/tex] and [tex]P(0) = P(3)[/tex]
[tex]P(0) + P(1) + P(1) + P(0) = 1[/tex]
[tex]2P(1) + 2P(0) = 1[/tex]
Substitute [tex]P(0)= 2P(1)[/tex]
[tex]2P(1) + 2*2P(1) = 1[/tex]
[tex]2P(1) + 4P(1) = 1[/tex]
[tex]6P(1) = 1[/tex]
Solve for P(1)
[tex]P(1) = \frac{1}{6}[/tex]
To calculate others, we have:
[tex]P(2) = P(1)[/tex]
[tex]P(2) = P(1) = \frac{1}{6}[/tex]
[tex]P(0)= 2P(1)[/tex]
[tex]P(0) =2 * \frac{1}{6}[/tex][tex]P(0) =\frac{1}{3}[/tex]
[tex]P(3) = P(0) =\frac{1}{3}[/tex]
Hence, the PMF is:
[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {P(x)} & {1/3} & {1/6} & {1/6} & {1/3} \ \end{array}[/tex]
See attachment (1) for histogram
Solving (c): The CDF ; F(x)
This is calculated as:
[tex]F(x) = P(X \le x) =\sum\limit^{3}_{x_i \le x} P(x_i)[/tex]
For x = 0;
We have:
[tex]P(X \le 0) = P(0)[/tex]
[tex]P(X \le 0) = 1/3[/tex]
For x = 1
[tex]P(X \le 1) = P(0) + P(1)[/tex]
[tex]P(X \le 1) = 1/3 + 1/6[/tex]
[tex]P(X \le 1) = 1/2[/tex]
For x = 2
[tex]P(X \le 2) = P(0) + P(1) + P(2)[/tex]
[tex]P(X \le 2) = 1/3 + 1/6 + 1/6[/tex]
[tex]P(X \le 2) = 2/3[/tex]
For x = 3
[tex]P(X \le 3) = P(0) + P(1) + P(2) + P(3)[/tex]
[tex]P(X \le 3) = 1/3 + 1/6 + 1/6 + 1/3[/tex]
[tex]P(X \le 3) = 1[/tex]
Hence, the CDF is:
[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ {F(x)} & {1/3} & {1/2} & {2/3} & {1} \ \end{array}[/tex]
See attachment (2) for histogram
Related Questions
Solve the compound inequality.
7x>-35 and -5x ≥ -50
A. -5< x≤10
B. -5≤x≤10
C. 5≤x≤10
D. 5>x≤10
need help
Answers
Answer:
A. -5< x≤10
Step-by-step explanation:
7x>-35 and -5x ≥ -50
7x>-35
x>-5
-5x ≥ -50
x≤ 10
so, the result is:
-5< x ≤10
HELLO CAN SOMEONE HELP ME! MATH :) NO FAKE ANSWERS PLS :D
Answers
Answer:
60 cm²Step-by-step explanation:
The area is:
A = 12*6 - 3*4 = 60 cm²Answer:
[tex]60cm {}^{2} [/tex]
A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4 6 5 7 3 5 What is the best explanation of how to find the experimental probability of rolling a 3? To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary.
Answers
Number Frequency Probability
1 4 0.13
2 6 0.20
3 5 0.17
4 7 0.23
5 3 0.10
6 5 0.17
total 30 1.00
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary.
5/30 = 1/6 or 0.166 or 16.6% or 17%.
Plsss answer this quick question!!
Answers
Answer:
D
Step-by-step explanation:
i would say D because in the hall she would still be able to see the people where as if they are on a piece of paper in a box she cant see who will be drawn.
Answer:
B.
Step-by-step explanation:
A. Incorrect because it’s unreasonable.
C. Incorrect because why would a teacher pull 2 students from a completely different class to read?
D. Incorrect because does a teacher do that just to ask 2 students to do something simple?
B. The most reasonable answer that most teachers will do.
five plus three plus five to the second power times five minus two
question off of moby max
Answers
5 + 3 = 8 + 5^2 = 33 • 5 = 165 - 2 = 163
Final answer: 163
What do I put in 1,2,3,4,5,6 I need help plz timed test
Answers
Answer:
The value of x = 6.5 units
Step-by-step explanation:
Given triangle is a right angle triangle;
Length of base = 2.5 unit
Length of perpendicular = 6 unit
Find:
The value of x
Computation:
Using Pythagoras theorem;
Hypotenuse² = Base² + Perpendicular²
Hypotenuse² = 2.5² + 6²
Hypotenuse² = 6.25 + 36
Hypotenuse² = 42.25
Hypotenuse = √42.25
Hypotenuse = 6.5 unit
The value of x = 6.5 units
I REALLY NEED HELP , “ a company is designing a new cylindrical water bottle. the volume of the bottle will be 207 cm *to the 3rd power* the height of the water bottle is 8.4 cm. what is the radius of the water bottle?”
Answers
Answer:
Radius, r = 2.80 cm
Step-by-step explanation:
Given the following data;
Volume of cylinder = 207 cm³
Height = 8.4 cm
Pie, π = 3.14
To find the radius of the water bottle;
Mathematically, the volume of a cylinder is given by the formula;
V = πr²h
Where;
V is the volume of a cylinder.
r represents the radius of the cylinder.
h represents the height of the cylinder.
Substituting into the formula, we have;
207 = 3.14 * r² * 8.4
207 = 26.376r²
r² = 207/26.376
r² = 7.85
r = √7.85
Radius, r = 2.80 cm
A red pebble is equal to 3 yellow pebbles a blue pebble is equal to a red and 2 yellow pebbles a green is equal to 3 red pebbles. What is the value in pebbles of a green pebble and a blue pebble divided by 2 red pebbles and a yellow pebble
Answers
Answer: 2
Step-by-step explanation:
Given
Red pebble is equal to 3 yellow pebble
A blue marble is equal to a red pebble and 2 yellow pebble
A green pebble is equal to 3 red pebble
Suppose [tex]R,B,Y,G[/tex] represents red, blue, yellow, and green pebbles
[tex]\therefore R=3Y\\B=R+2Y\\G=3R[/tex]
Express Red in terms of yellow in blue pebble equation
[tex]B=3Y+2Y\\B=5Y[/tex]
Now, express Green Pebble in terms of yellow pebble
[tex]G=3R=3(3Y)\\G=9Y[/tex]
Value of
[tex]\Rightarrow \dfrac{G+B}{2R+Y}\\\\\Rightarrow \dfrac{9Y+5Y}{2\times 3Y+Y}\\\\\Rightarrow \dfrac{14Y}{7Y}=2[/tex]
Which of the following expressions has the greatests value?
Answers
HELP
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answers
Answer:
It's Tan.
Multiple Thumbs-up ^_^
We want the following inequality to be true: IMAGE BELOW!
Answers
Answer:
B. X=7
Step-by-step explanation:
Because 9 greater than 7
Write the absolute value equation that is represented by the graph
Answers
Answer:
y = |x + 2| - 5
Step-by-step explanation:
ASAP PLEASE HELP FAST if you can do any of them please do
Answers
Answer:
Number 7: D. 378 ft
And I'm Not Sure About The Others
Step-by-step explanation:
Answer:
question 8 : 157 m²
Step-by-step explanation:
cone volume:. π×r²×h/3
3,14×25×6/3 = 157 m²
Mandy works part-time to earn money for a trip. The amount she saves after working x hours is given by the equation y=7.5x+40. How much does Mandy earn per hour?
Answers
[tex]y = 7.5x + 40 \\ y = 7.5(1) + 40 \\ y = 7.5 + 40 \\ y = 47.5[/tex]
[tex]mandy \: earns \: 47.5 \: per \: hour[/tex]
someone help
NO LINK IM SO FR NO LINKS
Answers
Answer:
I think iit's no consistent
Step-by-step explanation:
no consistent because there is no multiplying happening and no consistent adding happening
If adult grey whales weigh an average of 50 - 55 tons, about how many pounds does an adult grey whale weigh? (A ton equals 2000 pounds.)
Answers
Answer:
100000
Step-by-step explanation:
First multiplt the given njmber with 2000 and subrat total number givem
Answer: c
Step-by-step explanation:
Determine whether AB is tangent to the circle with center c
Answers
9514 1404 393
Answer:
yes, no, no
Step-by-step explanation:
The triangle will be a right triangle if the sum of the squares of the two short sides, less the square of the long side, is zero. (This is what the Pythagorean theorem tells you.) The angle where the radius meets the circle must be a right angle if the line is to be a tangent.
__
a) 3^2 +4^2 -5^2 = 9 + 16 -25 = 0 . . . . AB is a tangent
__
b) 9^2 +15^2 -18^2 = 81 +225 -324 = -18 . . . . AB is not a tangent
__
c) 10^2 +48^2 -52^2 = 100 +2304 -2704 = -300 . . . . AB is not a tangent
how many kilometers rode her bike in x minutes?
Answers
its g, yww .
5 = 0.5
10 = 1.0
15 = 1.5
20 = 2.0
25 = 2.5
Samir bought 3 pounds of cement to repair the cracks in his sidewalk.
Each crack needs to be filled with 2 ounces of cement.
Answers
Answer:
The answer is 24 cracks will be filled
Step-by-step explanation:
hope it helps :3
16 ounces in a pound. convert pounds to ounces
calculate the amount of cement we have. That would be 3 x 16 = 48 ounces of cement.
The amount of cracks to be filled : 48 /2 = 24 cracks
Find the volume of the composite solid.
Answers
Answer:
2960 ft³
Step-by-step explanation:
Rectangular prism = 12x20x10=2400
Rectangular pyramid = 1/3x12x20x7=560
2400+560=2960
How to find y intercept without a graph HELP
Answers
Answer:
You need to use the graph's equation and find the answer of y when x is 0 as this will give y when it is on the y axis.
To do this, substitute in 0 were x is in the equation and you will find the y intercept
The triangle and the rectangle have the same area
calculate the value of w.
Show your working
Answers
Answer:
2.5 cm
Step-by-step explanation:
6*5=30
30/2=15
That's the area of the triangle
The area of the rectangle must also equal 15
6*w=15
Divide by both sides by 6
This gives you: 2.5
The value of the width of rectangle w for which the triangle and the rectangle have the same area is, 2.5 cm
Used the formula of area of the rectangle and area of the triangle which states that,
Area of rectangle = Length × Width
And, Area of triangle = 1/2 × Base × Height
Given that,
The triangle and the rectangle have the same area.
Here, in a triangle;
Base = 5 cm
Height = 6 cm
So, the Area of the triangle is,
[tex]A = \dfrac{1}{2} \times 5 \times 6[/tex]
[tex]A = 15 \text{ square cm}[/tex]
In a rectangle;
Length = 6 cm
Width = w cm
So, the area of a rectangle,
[tex]A = 6 \times w[/tex] [tex]\text{ square cm}[/tex]
Since the triangle and the rectangle have the same area.
So, equate both the area of the triangle and rectangle,
[tex]6 \times w = 15[/tex]
Divide both sides by 6,
[tex]w = \dfrac{15}{6}[/tex]
[tex]w = 2.5 \text{ cm}[/tex]
So, the value of w is 2.5 cm
To learn more about the triangle visit;
brainly.com/question/1058720
#SPJ4
Paula is draining her fish tank.
When she starts draining it, the height of the water is 33 cm.
Six minutes later, the height of the water is 15 cm.
Question: If the water continues to drain
at this rate until it is empty, how many
total minutes will it take Paula to drain
her fish tank?
Answers
Answer:
If the water continues to drain at this rate, it would take 11 total minutes for Paula to drain her fish tank.
Step-by-step explanation:
In 6 minutes, she is able to drain 18 cms of her fish tank, so in 1 minute, she would be able to drain 3 cms of her fish tank. 15 divided by 3 is 5, so it would take 5 minutes to drain the rest of her fish tank. But it is asking for the total amount so 5 plus 6 is 11 total minutes.
Mr. Claussen needs a total of 15 pounds of ground beef to make hamburgers for a company picnic. He finds that 2 pounds of ground beef cost $4.40.At this rate, how
much should Mr. Claussen plan on spending for the 15 pounds of ground
beef?
A $66.00
B. $33.00
C. $19.40
D. $2.20
Answers
Answer: your answer should be 33.00/B
Step-by-step explanation:
Because u need to divide 15 by 2 = 7.5
Then Times that my 4.40
U get 33 dollar
Can anyone help? I’ll give Brainly! Thank you :)
Answers
==============================================================
Explanation:
f(x) is equal to both x^2-2x+3 and also -6x at the same time. Set those two expressions equal to one another and solve for x.
x^2-2x+3 = -6x
x^2-2x+3+6x = 0
x^2+4x+3 = 0
(x+3)(x+1) = 0 .... see note below
x+3 = 0 or x+1 = 0
x = -3 or x = -1
Note: 3 and 1 multiply to 3, and also add to 4.
---------------------
Once we get the x values, we plug them into either equation to find the y value.
So if x = -3, then
f(x) = x^2-2x+3
f(-3) = (-3)^2-2(-3)+3
f(-3) = 9 + 6 + 3
f(-3) = 18
or we could say
f(x) = -6x
f(-3) = -6(-3)
f(-3) = 18
Both versions produce the same output when x = -3.
The second version is easier to work with.
Since x = -3 leads to y = 18, we know that (-3, 18) is one of the solutions. That explains where your teacher got (-3, 18) from.
-----------
We'll use this idea for x = -1 now
f(x) = x^2-2x+3
f(-1) = (-1)^2-2(-1)+3
f(-1) = 1 + 2 + 3
f(-1) = 6
or we could say
f(x) = -6x
f(-1) = -6(-1)
f(-1) = 6
Like before, both versions of f(x) produce the same output when the input is x = -1.
The other solution is (-1, 6)
Find the whole number equal to the fraction below. Enter your answer in the space provided. 21 /3
Answers
Answer:
the answer is 7
Step-by-step explanation:
divide the numerator (21) by the denominator (3) and you will get 7 as the answer hope this helped
12 divided by 1 1/5 plz hurry asap
Answers
Answer:
10
Step-by-step explanation:
Answer:
10 :)
Step-by-step explanation:
12 divided by 1 1/5 is the same as:
It is always easier to convert the fraction into a decimal:
like we converted 1/5 into .20.
[tex]\frac{12}{1.2}[/tex]=10
A question you can ask yourself is:
How many times can you multiply 1.2 to get 12?
1.2*10=12.
Hope it helps! :))
If 3x + 10 = 10 + 2x, what is the value of x?
A) x = 4
B) x = -4
C) x = -1
D) x = 0
Answers
Answer:
x=0
Step-by-step explanation:
3x + 10 = 10 + 2x
Subtract 2x from each side
3x-2x + 10 = 10 + 2x-2x
x+10 = 10
Subtract 10 from each side
x+10-10 = 10-10
x=0
Answer:
x=0
Step-by-step explanation:
3x + 10 = 10 + 2x
Subtract 2x from each side
3x-2x + 10 = 10 + 2x-2x
x+10 = 10
Subtract 10 from each side
x+10-10 = 10-10
x=0
Simplify: [3(2a)3/2] 2
Answers
Answer:
2=18a
Step-by-step explanation:
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
Answers
Answer:
He showed that f(n) ÷ f(n - 1) was a constant ratio.
Given that Jake has proved that a function f(x) is a geometric sequence.
GEOMETRIC SEQUENCE: A geometric sequence is a sequence of numbers where each term is found by multiplying the preceding term by a constant called the common ratio, r.
So, in Jame's proof, he showed that each term is multiplied by a constant to get the next term.
That is, if 'c' is the constant that was used in the proof, then we must have
This implies that
Therefore, he showed that f(n) ÷ f(n - 1) was a constant ratio.