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
allsm [11]
3 years ago
9

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

g the route. The first service station is located 20 miles from city A, and the second service station is located 30 miles from city B. If the bus breaks down at a random point along the route, find the expected value of the distance of the bus from the nearest service station.
Mathematics
1 answer:
melamori03 [73]3 years ago
3 0

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.  

X~ Uniform(0,100)

Then the probability mass function is given as follows.

f(x) = P(X=x) = 1/100  \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0  \,\,\,\, \text{otherwise}

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located  70 meters away from city A then the mid point between 20 and 70  is (70+20)/2 = 45 then we can represent D as follows

D(x) =\left\{ \begin{array}{ll}  x  & \mbox{if } 0\leq x \leq 20 \\  x-20 & \mbox{if } 20\leq x < 45\\                70-x & \mbox{if } 45 \leq x \leq 70\\                x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable Y = D(X), Y is a random variable as well, remember that there is a theorem that says that

E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx

Where f(x) is the probability mass function of X. Using the information of our problem

E[Y] = \int\limits_{-\infty}^{\infty}  D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx  \bigg]\\= \frac{51}{4} = 12.75

You might be interested in
What is the square root of twenty-five
AURORKA [14]
The square root of 25 would be 5!

Brainliest please? I am trying to get my rank to ace!
7 0
3 years ago
An experiment consists of tossing a coin and drawing a card, with the card- drawing stage dependent on the results of the coin t
Mnenie [13.5K]

Answer:

52 is the size of the sample space of this two-stage experiment

3 0
2 years ago
Wich function is described by the value in the table​
kolbaska11 [484]
The table isn’t shown so I cant tell
3 0
2 years ago
it took a submarine 30 seconds to sink 225 feet, moving at a constant speed. The captain wants to know how much feet does he the
icang [17]

Answer:

Dont count me if I'm wrong but if you divide 225 by 30 you get 7.5

So your answer should be 7.5

4 0
2 years ago
A car travels 50 km in 2 liters find
Savatey [412]
It can travel 125km with 5 liters
And 6 liters to travel 150 :)
5 0
2 years ago
Read 2 more answers
Other questions:
  • How can I simplify 1/2 + 2/3. Do I add,then divide.
    11·2 answers
  • Solve system by substitution x-5y=18 2×+6y=4
    5·1 answer
  • What is 0.97 estimated to?
    8·1 answer
  • If a circle has a circumference of C, what is the area of the circle in terms of C? A. A=πC
    7·1 answer
  • Emily can spend no more than $40.00 on a raincoat. Sales tax is 8.25% of the marked price. Can Emily afford a raincoat priced at
    5·1 answer
  • chris is making a table top.feom some leftover tiles.he has 9 tiles that measures 3 1\8 inches long and 2 3\4 inches wide.what i
    13·1 answer
  • I need help with this equation it's confusing
    11·2 answers
  • What is the slope of the line that is parallel to the line represented by the equation below? 4x-5y=-1 A. 4/5 B. -4/5 C. 5/4 D.
    14·1 answer
  • F(x)=x^2 linear or exponential
    5·1 answer
  • Find the equation of tangent and normal to the circle 2x² + 2y² -7x +4y - 3= 0 at (3/2, 3)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!