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
Viefleur [7K]
2 years ago
5

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with t

wo hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
Y
p(x,y) 0 1 2
x 0 0.10 0.04 0.02
1 0.08 0.20 0.06
2 0.06 0.14 0.30

a. What is P(X = 1 and Y = 1)?
b. Compute P(X ≤ 1 and Y ≤ 1).
c. Give a word description of the event {X ≠ 0 and Y ≠ 0}, and compute the probability of this event.
d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X ≤ 1)?
e. Are X and Y independent rv’s? Explain.
Mathematics
1 answer:
zaharov [31]2 years ago
7 0

Answer:

a. 0.2

b. 0.42

c. 0.7

d. the solution is in the explanation

e. x and y are not independent

Step-by-step explanation:

a. from the joint probability mass function table,

p(x=1) and p(Y= 1)

= p(1,1) = 0.2

b. prob(0,0)+prob(0,1)+prob(1,0)+prob(1,1)

= 0.10 + 0.04 + 0.08 + 0.20

= 0.42

P(X ≤ 1 and Y ≤ 1) = 0.42

c. prob {X ≠ 0 and Y ≠ 0}

= prob(1,1) + prob(1,2) + prob(2,1) + prob(2,2)

= 0.20 + 0.06 + 0.14 + 0.30

= 0.7

d. we have to calculate the marginal pmf of x and y here.

<u>we have the x values as 0,1,</u>2

prob(x=0) = 0.1 + 0.04 + 0.02

= 0.16

prob(x=1) = 0.08 + 0.2 + 0.06

= 0.34

prob(x=2) = 0.06+0.14+0.3

= 0.50

<u>we have y values as 0,1,2</u>

prob(y=0) = .1+.08+.06

= 0.24

prob(y=1) = .04+.2+.14

= 0.38

prob(y = 2) = 0.02+0.06+0.3

= 0.38

P(X ≤ 1) = prob(x=0)+prob(x=1)

= 0.34+0.16

= 0.50

e. from the joint table we have this,

prob(1,1) = 0.2

prob(x=1) = 0.34

prob(y=1) = 0.38

then prob(x=1)*prob(y=1)

= 0.34*0.38

= 0.1292

therefore prob(1,1) is not equal to prob(x=1)*prob(y=1)

0.2≠0.1292

x and y are not independent

You might be interested in
Find S5 for a geometric series for which a1=81 and r=1/9.
Minchanka [31]

ANSWER

S_5=91\frac{10}{81}




EXPLANATION


The sum of the first n terms of a geometric sequence is given by;


S_n=\frac{a_1(1-r^n)}{1-r} ,-1


Where n, is the number of terms and a_1 is the first term.


When n=5, we have a_1=81, we get;


S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}


S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}


S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}




S_5=\frac{7381}{81}


S_5=91\frac{10}{81}




6 0
3 years ago
Pls only put the right answer
Makovka662 [10]

Answer:

100°

Step-by-step explanation:

No explanation, by  your request.

3 0
2 years ago
What is the slope? (IXL)
andrey2020 [161]

Answer:

1/3

Step-by-step explanation:

rise over run

6 0
3 years ago
Enter the giveaway for points
Nookie1986 [14]

Answer:

Thxx for points how do I enter

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
When listing the domain (and range), we<br> list the repeated numbers
svetoff [14.1K]

Answer:hope help

Step-by-step explanation:

Find the range by listing all the y values from the ordered pairs. Repeated values within the domain or range don't have to be listed more than once. In order for a relation to be a function, each x must correspond with only one y value.

8 0
2 years ago
Read 2 more answers
Other questions:
  • A carpenter is building a rectangular fence for a playground. One side of the playground is the wall of a building 70 ft. wide.
    12·1 answer
  • Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the age of each.
    8·2 answers
  • Find the three angles of the triangle formed using the position vectors i hat − j 4k and i hat 2j 3k and the line segment connec
    12·1 answer
  • What is slime without water in it.
    12·1 answer
  • Will award Brainliest and extra points to whoever can get me the correct answer the fastest:
    11·1 answer
  • Elizabeth completely covered a square wall using 98.5ft squared with blue paint. which measurement is closest to the side length
    14·2 answers
  • Amy is biking to school from her father's house and Jeremy is biking to school from his aunt's house. Suppose Amy is moving at a
    5·1 answer
  • Evaluate the expression below.<br><br> 7×3−4×(225÷32)×2
    10·1 answer
  • The graph below shows the price of different numbers of mats below at a store:
    13·1 answer
  • Suppose a simple random sample of size n is drawn from a large population with mean and standard deviation. The sampling distrib
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!