Complete Question
Random variable X has CDF given as follows
[tex]F(x)_x = \left \{ {{{{{{{ 0 \ \ \ \ \ \ \ \ \ \ x < 0} \atop {\frac{8}{33}} \ \ \ \ \ \ 0 \le x \le 1} \atop{ \frac{5}{11} }\ \ \ \ \ 1 \le x \le 2 } \atop {\frac{7}{11} } \ \ \ \ \ \ 2 \le x \le 3} \atop{ \frac{26}{33} }\ \ \ \ \ 3 \le x \le 4 }\atop {\frac{10}{11} } \ \ \ \ \ \ 4 \le x \le 5} \atop{ 1}\ \ \ \ \ \ \ \ 5 \le x } \right.[/tex]
Find the PMF of X.Find the PMF of X, and confirm that it is a valid PMF.
Answer:
Generally the PMF is
X 0 1 2 3 4 5
P(X = x) [tex]\frac{8}{33}[/tex] [tex]\frac{7}{33}[/tex] [tex]\frac{2}{11}[/tex] [tex]\frac{5}{33}[/tex] [tex]\frac{4}{33}[/tex] [tex]\frac{1}{11}[/tex]
Generally to prove the validity of the PMF we add the probabilities , if it is equal to 1 then the PMF is valid otherwise , the PMF is not valid
So
[tex]\sum P(X = x) = \frac{8}{33} + \frac{7}{33} + \frac{2}{11} + \frac{5}{33} + \frac{4}{33}+ \frac{1}{11}[/tex]
[tex]\sum P(X = x) =1[/tex]
Hence the PMF is valid
Step-by-step explanation:
Generally the probability of X = 0 is evaluated as
[tex]P(0) = F(0) \ \ (for \ x \le 0) - F(0) \ ( for \ x < 0)[/tex]
=> [tex]P(0) = \frac{8}{33} - 0[/tex]
=> [tex]P(0) = \frac{8}{33}[/tex]
Generally the probability of X = 1 is evaluated as
[tex]P(1) = F(1) \ \ (for \ 1 \le 0) - F(1) \ ( for \ x < 1)[/tex]
=> [tex]P(1) = \frac{5}{11} - \frac{8}{33}[/tex]
=> [tex]P(1) = \frac{7}{33}[/tex]
Generally the probability of X = 2 is evaluated as
[tex]P(2) = F(2) \ \ (for \ 2 \le x ) - F(2) \ ( for \ x < 2)[/tex]
=> [tex]P(2) = \frac{7}{11} - \frac{5}{11}[/tex]
=> [tex]P(2) = \frac{2}{11}[/tex]
Generally the probability of X = 3 is evaluated as
[tex]P(3) = F(3) \ \ (for \ 3 \le x ) - F(3) \ ( for \ x < 3)[/tex]
=> [tex]P(3) = \frac{26}{33} - \frac{7}{11}[/tex]
=> [tex]P(3) = \frac{5}{33}[/tex]
Generally the probability of X = 4 is evaluated as
[tex]P(4) = F(4) \ \ (for \ 4 \le x ) - F(4) \ ( for \ x < 4)[/tex]
=> [tex]P(4) = \frac{10}{11} - \frac{26}{33}[/tex]
=> [tex]P(4) = \frac{4}{33}[/tex]
Generally the probability of X = 5 is evaluated as
[tex]P(5) = F(5) \ \ (for \ 5 \le x ) - F(5) \ ( for \ x < 5)[/tex]
=> [tex]P(5) = 1- \frac{10}{11}[/tex]
=> [tex]P(5) = \frac{1}{11}[/tex]
Generally the PMF is
X 0 1 2 3 4 5
P(X = x) [tex]\frac{8}{33}[/tex] [tex]\frac{7}{33}[/tex] [tex]\frac{2}{11}[/tex] [tex]\frac{5}{33}[/tex] [tex]\frac{4}{33}[/tex] [tex]\frac{1}{11}[/tex]
Generally to prove the validity of the PMF we add the probabilities , if it is equal to 1 then the PMF is valid otherwise , the PMF is not valid
So
[tex]\sum P(X = x) = \frac{8}{33} + \frac{7}{33} + \frac{2}{11} + \frac{5}{33} + \frac{4}{33}+ \frac{1}{11}[/tex]
[tex]\sum P(X = x) =1[/tex]
Hence the PMF is valid
In Algebra, we learn about functions of various types. These functions are often seen in a progression from least complicated (linear) to most complicated (piecewise with nonlinear parts). And then there are other types of functions in-between: exponential, quadratic, polynomial, radical, and logarithmic. But with all their differences and unique properties, these share a common trait of being functions that we can graph in a coordinate plane.
What are some other things you can observe to have that same quality of functions: unique, but sharing a common trait or purpose?
Somethings I can observe that have the same quality is that all functions only have one outcome for a given input. A vertical line will never meet the graph more than once. No X values are used more than once. A function will have either no horizontal asymptote or just one asymptote. These are some common traits that all functions have.
We can see that all functions have the one outcome for one value of x if we can see all the functions carefully.
What is a function?
A function is a relation in which each value of x corresponds to some value of y.
How to determine the features of a function?
When we see some functions, they have the same quality of giving one result for one input. The quality of the graph of all functions is that the vertical line cannot meet the axis twice.
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[tex] \frac{3}{8} + \frac{1}{7} [/tex]
cual es el resultado?
Answer:
El resultado es:
[tex]\displaystyle \frac{29}{56}[/tex]
Step-by-step explanation:
Suma de fracciones
Vamos a sumar:
[tex]\displaystyle \frac{3}{8}+\frac{1}{7}[/tex]
Debemos encontrar el mínimo común múltiplo (MCM) entre los denominadores, en este caso, 7 y 8.
Descomponemos en factores primos:
7=7
8=2*2*2
Se toman los comunes y no comunes con máximo exponente, así que el MCM es 7*8=56.
Se procede a dividir el MCM entre cada denominador y al multiplicarlo por su numerador correspondiente:
[tex]\displaystyle \frac{3}{8}+\frac{1}{7}=\frac{3*7+1*8}{56}=\frac{29}{56}[/tex]
El resultado es:
[tex]\displaystyle \frac{29}{56}[/tex]
Solve this please to get brainliest
I can be late, I can be early, I can be astronomical or atomic and my insides are incredibly complex. What am I?
Answer:
Clock
Step-by-step explanation:
The answer is Clock because the time changes from AM to PM and there are many things inside that cause it to work.
2x-1/15=7.2/3 Find x
Answer:
x = 18.5
Step-by-step explanation:
If you do the butterfly method, you should get 2x-1 = 36
2x = 37
x = 18.5
Math help! DUE IN 30 MINUTES (50 points)
Answer: i won't tell you the answer but i will break it up for you so i can make easier for you
Step-by-step explanation: (-5x^2) (y^c) x (x^5) (2y^3)(5x^7)(y^6)(2) Or for the ones for numerator and denominator you can do this
(x^5)
____ = ( -5x^7)
______
(2)
(2y^3)
So for the one with numerator and denominator i got a stuck on a little but i tried doing this way if you like this way i can keep it like this if you dont i can change it
Josh rents a kayak at a nearby state park. He pays a flat rate of $12.99 plus $3.75 for each hour that he spends in the water. Josh spends 4.5 hours on the river. How much did he spend?
HELP ASAP
IDK WHAT THIS IS HELP
Answer:
b. [tex]\frac{13}{6}[/tex]
Step-by-step explanation:
(15, 3) (9, -10)
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\frac{-10 + -3}{9 - 15}[/tex]= [tex]\frac{-13}{-6}[/tex] = [tex]\frac{13}{6}[/tex]
rounding to the nearest tenth, which of the following give an overestimate?
45.07 × 3.45
19.74 × 5.53
8.16 × 60.29
2.92 × 77.81
32.86 × 10.4
1. 157.5108.35
2. 108.35
3. 494.46
4. 233.7
5. 342.16
Step-by-step explanation:
Someone please help
Me with this
Answer:
y= 1/3x + 1.
Step-by-step explanation:
HELP ME PLEASE!! This is due today!! Use kcf and show ur work plzz!
Answer:
[tex]\frac{3}{2} \textrm{ cups of flour}[/tex]
Step-by-step explanation:
the ratio of cups of flour per 1 cup of water:
[tex]\frac{2\frac{1}{2}}{1\frac{2}{3}}=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{3}{2}[/tex]
What is the answer to
1 + 3(8.63) =
Answer:
26.89
Step-by-step explanation:
what is the bed what is it
Answer:
A bed is a type of object a person uses to sleep on. It usually contains blankets and pillows
Step-by-step explanation:
Can i have brainliest?
A goose is flying horizontally at an altitude of 300 ft and a speed of 50 ft/sec passes directly over a pond. Find the rate at which the distance from the goose to the pond is increasing when it is 500 ft away from the pond.
Answer:
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Step-by-step explanation:
We assume that goose is flying at constant velocity. After reading carefully the statement of the problem, we create the following geometrical diagram, which is included at the end of this explanation and represents the following Pythagorean identity:
[tex]x^{2}+y^{2} = r^{2}[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Horizontal distance of the goose from pond, measured in feet.
[tex]y[/tex] - Vertical distance of the goose from pond, measured in feet.
[tex]r[/tex] - Resultant distance of the goose from pond, measured in feet.
We find the rate of change in time at which resultant distance is increasing by differentiating on (Eq. 1):
[tex]2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y = 2\cdot r \cdot \dot r[/tex]
[tex]x\cdot \dot x + y\cdot \dot y = r\cdot \dot r[/tex]
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (Eq. 2)
Where:
[tex]\dot x[/tex] - Rate of change of horizontal distance, measured in feet per second.
[tex]\dot y[/tex] - Rate of change of vertical distance, measured in feet per second.
[tex]\dot r[/tex] - Rate of change of resulting distance, measured in feet per second.
If we know that [tex]x = 500\,ft[/tex], [tex]y = 300\,ft[/tex], [tex]\dot x = 50\,\frac{ft}{s}[/tex] and [tex]\dot y = 0\,\frac{ft}{s}[/tex], the rate at which the distance from the goose to the pond is increasing is:
[tex]\dot r = \frac{(500\,ft)\cdot \left(50\,\frac{ft}{s}\right)+(300\,ft)\cdot \left(0\,\frac{ft}{s} \right) }{\sqrt{(500\,ft)^{2}+(300\,ft)^{2}}}[/tex]
[tex]\dot r \approx 42.875\,\frac{ft}{s}[/tex]
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Answer all of these questions correctly. Will give brainliest.
Answer:
1-5
3-7
8-4
2-6
6-3
3-7
Step-by-step explanation:
Imagine an element that has 15 protons, 16 neutrons, and 18 electrons. Which of the following would NOT be considered an isotope of this element? *
15 protons, 16 neutrons, and 15 electrons
15 protons, 17 neutrons, and 15 electrons
15 protons, 15 neutrons, and 18 electrons
Answer:
15 protons, 15 neutrons and 18 electrons (3rd one) is the answer
Step-by-step explanation:
Which expression is equivalent to 1/3 p + 15
1/3 (p+45)
1/3 (p+5)
3 (p+45)
3(p+5)
Answer:
[tex]1/3 (p+5) [/tex]
Step-by-step explanation:
[tex]1/3 p + 15 = \frac{1}{3} p + 15 = \\ \frac{p + 5}{3} = \frac{1}{3} ( p+ 5)[/tex]
♨Rage♨
If twice the number, added to 3 is divided by the number plus 9, the result is three halves. Find the number
Answer:
x=21
Step-by-step explanation:
(3+2x)/(x+9)=3/2
(x+9)(3+2x)=(3/2)(x+9)
3+2x=(3x+27)/2
2(3+2x)=3x+27
6+4x=3x+27
x=21
SHNERPY GERPBY
Put the steps of the Electoral College Process in order.
Question 5 options:
First candidate to 270 electoral votes wins the presidency.
Electors cast the official vote.
Popular vote.
Whoever wins the state, gets all of that state's electoral votes.
Answer: (number 1 is the popular vote) (number 2 is whoever wins the state gets all the electoral votes) (number 3 is electors cast the official vote) (and finally at number 4 the first candidate to 270 wins the election)
please answer this!
giving brainliest
Answer:
5. 65
6. 80
7. m<7 and m<2
Suppose you purchase a car using an installment loan for $26,000 for 48 months at 5% annual rate. Your payment is $598.76. Which is nearest to the total finance charge?
Answer:
7
Step-by-step explanation:
solve for x explain pls
6+2x+31=x+26
Personal Finances Practice Active 1 2 You are starting a new job in sales for the company Buy 'n Large. Your hourly wage is $10.00 per hour and you get time and a half for anything over 40 hours. Based on a 5-day work week, 8-hour day, and 52 week year, determine your annual gross base salary a $21,650 C. $20,800 b. $18,798 d. $19,980
Answer:
C.20,800
Step-by-step explanation:
10.00 per hour so 10x8=80
then 80x5=400
400x52=20,800
In Fairbanks, Alaska, the average temperature in January is -9.7°F. The
average temperature in July is 62.4°F. On average, how many degrees
colder is Fairbanks in January than in July?
Answer:
72.1 degrees... 72 point 1 degress in case you cant see the ( . )
Step-by-step explanation:
62.4 minus -9.7= is 72.1
Does the set of ordered pairs {(0,4),(2,6),(4,2), (6,2), (8,6)} represent a function?
Answer:
yes it does
Step-by-step explanation:
the x numbers do not repeat
Yes, the given relation is function.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
set of ordered pairs= {(0,4),(2,6),(4,2), (6,2), (8,6)}
As, we know that the function has one input with corresponding one output.
So, we can see from the ordered pair that no input value have repeated and have respective output.
Hence, the relation is function.
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At a certain intersection, the traffic light is red for 15 seconds, yellow for 5 seconds and green for 30 seconds. Find the probability that, of the next eight cars that arrive randomly at the light, exactly three will be stopped by a red light.
Answer: 0.254
Step-by-step explanation:
Given that:
Number of cars = number of trials (n) = 8
Number that will be stopped by a red light = Numbe rof successes (r) = 3
Probability of success :
Red light = 15 seconds ; yellow = 5 seconds ; green = 30 seconds
P(red) = p(success) = p = 15 / (15 + 5 + 30) = 15/50 = 3 /10 = 0.3
1 - p = 1 - 3/10 = 7/10 = 0.7
Using the binomial probability relation:
p(exactly 3):
P(8, 3) = 8C3 * p^3 * (1-p)^(8-3)
P(8, 3) = 8C3 * p^3 * (1-p)^5
P(8, 3) = 56 * 0.3^3 * 0.7^5
= 0.25412
= 0.254
Solve for x, y, and z in the figure below.
47° 58°
x
y° / 81°
zº
N
оа
Ob
Ос
x = 34, y = 99, z = 41
x = 41, y = 92, z = 41
x = 72, y = 61, z = 41
X = 63, y = 70, z = 41
Od
Answer:
Option (A)
Step-by-step explanation:
From the given triangle in the picture,
∠y and the angle measuring 81° is a pair of supplementary angles (linear pair angles).
m∠y + 81° = 180°
m∠y = 180° - 81°
= 99°
By the property of a triangle,
x° + y° + 47° = 180°
x° + y° = 180° - 47°
x° + y° = 133°
For y = 99°
x° + 99° = 133°
x° = 133° - 99°
= 34°
Similarly, z° + 58° + 81° = 180°
z° + 139° = 180°
z° = 180° - 139°
z° = 41°
Therefore, Option (A) will be the correct option.
Applying the definition of the straight line angle and sum of triangle, the values of the variables in the figure are:
x = 34, y = 99, z = 41Recall:
Angles on straight line = 180°Sum of triangle = 180°Thus:
y° + 81° = 180° (angles on a straight line)
Subtract 81 from each sidey° = 180° - 81°
y° = 99°
x° + y° + 47° = 180° (sum of triangle)
Substitutex° + 99° + 47° = 180°
x° + 146° = 180°
Subtract 146° from each sidex° = 180° - 146°
x° = 34°
z° + 81° + 58° = 180° (sum of triangle)
z° + 139° = 180°
Subtract 139° from each sidez° = 180° - 139°
z° = 41°
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Solve for x. What is the root? If there is no root, choose none.
Answer:
4
Step-by-step explanation:
A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)
Answer:
350.62 feet
Step-by-step explanation:
What is the image point of
(1,4)(1,4)
(1,4) after a translation left 5 units and down 5 units?
Answer:
(-4,-1)
Step-by-step explanation:
Sue sees 30 adult elephants and 18 baby elephants at the zoo. What is the ratio of adult elephants to baby elephants
Answer: 30:18 or 30 to 18
Step-by-step explanation: