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
aalyn [17]
3 years ago
9

A large but sparsely populated county has two small hospitals, one at the south end of the county and one at the north end. The

south hospital emergency room has four beds, whereas the north hospital emergency room has only 3 beds. Let X denote the number of south beds occupied at a particular time on a given day. Let Y denote the number of North beds occupied at the same time on the same day. Suppose that these two random variables are independent; that the pmf of X puts probability masses .1, .2, .3, .2 and .2 on x values of 0, 1, 2, 3, and 4 respectively; and that the pmf of Y distributes probabilities .1, .3, .4 and .2 on the y values 0, 1, 2, and 3, respectively.
(a) Display the joint pmf of X and Y in a joint probability table.
(b) Compute P(X ≤ 1 and Y ≤ 1) by adding probabilities from the joint pmf, and verify that this equals the product of P(X ≤ 1) and P(Y ≤ 1).
(c) Express the event that the total number of beds occupied at the two hospitals combined is at most 1 in terms of X and Y, and then calculate this probability.
(d) What is the probability that at least one of the two hospitals has no beds occupied?

Mathematics
1 answer:
Readme [11.4K]3 years ago
3 0

Answer:

Step-by-step explanation:

Probability distribution of this type is a vicariate distribution because it specifies two random variable X and Y. We represent the probability X takes x and Y takes y by

f(x,y) = P((X=x,Y=y) ,

and given that the random variables are independent the joint pmf isbgiven by:

f(x,y) = fX(x) .fY(y) and this gives the table (see attachment)

(b) the required probability is given by considering X=0,1 and Y =0,1

f(x,y) = sum{(P(X ≤ 1, Y ≤ 1) }

= [0.1 +0.2 ] × [0.1 + 0.3]

= 0.3 × 0.4

= 0.12

Now we find

fX(x) = sum{[f(x.y)]} for y =0, 1 and similarly for fY(y)= sum{[f(x,y)]} for x=0, 1

fX(x) = sum{[f(x,y)]}= 0.1+0.3

= 0.4

fY(y) = sum{[f(x.y)]} = 0.1 + 0.2

= 0.3

Since fY(y) × fX(x) = 0.4 × 0.3

= 0.12

Hence f(x,y) = fX(x) .fY(y), the events are independent

(c) the required event is give by: [P(X<=1, PY<=1)]

= P(X<=1) . P(Y<=1)

= [sum{[f(x.y]} over Y=0,1] × [sum{[f(x.y)]}, over X= 0, 1

= 0.4 × 0.3

= 0.12

(d) the required event is given by the idea that: either The South has no bed and the North has or the the North has no bed and the South has. Let this event be A

A =sum[(P(X = 1<= x<= 4, Y =0)] + sum[P(X =0 Y= 1 <= x <= 3)]

A = [0.02 + 0.03 + 0.02 + 0.02] + [0.03 + 0.04 + 0.02]

A = [0.09] + [ 0.09]

A = 0.18

Pls note the sum of the vertical column X=2 is 0.3

You might be interested in
PLEASE HELP! Oscar and Kim have $22.00 each to spend at a book fair, where all students receive a 30% discount. They both want t
babymother [125]

Answer:

Both of them correct.

$21.945

They have enough money to purchase the book

Step-by-step explanation:

Oscar takes 30% of the normal price and subtracts it from the normal price. Out of 100% price he takes 30% so the result is: 100-30%= 70% of the normal price. Oscar's first step has the same result as Kim.

Oscar takes 10% of the discounted price (70%) and adds it back. The price will become 70% + 10%*70%= 77% of original price. Kim multiplies the discounted price with 110%, so the price will be: 70% * 110%= 77%. Both also give the same result.

The final price is 77% of the original, it will be: $28.50* 77%= $21.945

Both of them can buy the book

3 0
3 years ago
Elsa pumped 12 gallons of water into her pool. This was done over a period of 2 minutes at a constant rate. What was the change
Rashid [163]

Answer:

it was 6 because do 12 / 2 will equal 6.

5 0
3 years ago
What is the product of 4 x 2/3
Genrish500 [490]

Answer:

Step-by-step explanation:

Remark

A good thing to understand is that when a whole number and a fraction are multiplied, the method is the same as multiplying 2 fractions. What that means is make the whole number into the numerator of a fraction and put a 1 where the denominator should be.

Solution

4/1 * 2/3 = 4*2 / 1 * 3 = 8/3

3 0
2 years ago
7×9-8+11-6 [5+2 (-3)]
kupik [55]
Ok, MissWalker! Please try your best to understand this, it may get confusing.
I have solved this on a different website, and here is my solving in a picture. I hope I helped!!! :D

8 0
3 years ago
This is due tm please help​
Mumz [18]

Answer:

25. No slope

Step-by-step explanation:

25. Y2 - Y1 / X2 - X1

= -8 - (-3) / 9 - 9

= -5 / 0

= no slope; straight line

Use this formula (Y2 - Y1 / X2 - X1) for each ques.

8 0
3 years ago
Other questions:
  • 1. Part A: Solve the inequality. Show work for full<br> credit.<br> 2x+3&lt;7
    11·2 answers
  • 2. Determine whether the relation is a function.
    11·1 answer
  • 43 Points
    12·2 answers
  • A town has a population of 12000 and grows at 3.5% every year. What will be the population after 7 years, to the nearest whole n
    15·1 answer
  • amal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.
    9·2 answers
  • Find the mean, median, and inter
    15·2 answers
  • I WILL GIVE BRAINLIEST<br> Evaluate the following expression.<br> 4 - (3 - 2)²
    11·2 answers
  • 3. In determining food spending, it was found that the average meal in Albany is normally distributed, with a mean of $40 and a
    7·1 answer
  • Greg has $2,571.68 in his bank account and makes automatic monthly rental payments of $321.46 for a car loan. If he stops making
    11·1 answer
  • Please help. I struggle on these so bad.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!