There are four balls with the same size in a box. The balls are numbered 1, 2, 3 and 4. Sonya randomly picks up one ball, puts i
t back, and then randomly picks up one ball from the box. Let denote the sum of the numbers on the two balls she picked up. Find (round off to second decimal place).
1 answer:
Answer:
Explanation:
Here we have sampling with replacement. There are 4 x 4 = 16 out comes each with equal probability 1/16 .
The sample space being {1,2,3,4} {1,2,3,4} .
The random variable X representing the sum of the numbers on the balls has values from 2 to 8.
The other detailed steps and appropriate analysis is shown in the attached file.
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Answer:
In equilibrium, total output by the two firms will be option e= 300.
Q = +
Q = 100 + 200
Q = 300
Explanation:
Data Given:
Market Demand Curve = P = 1660-4Q
where, P = price and Q = total industry output
Each firm's marginal cost = $60 per unit of output
So, we know that Q = +
where being the individual firm output.
Solution:
P = 1660-4Q
P = 1660- 4( +
)
P = 1660 - 4 - 4
Including the marginal cost of firm 1 and multiplying the whole equation by
Let's suppose new equation is X
X = 1660 - 4
- 4
- 60
Taking the derivative w.r.t to , we will get:
= 1660 - 8
- 4
- 60 = 0
Making rearrangements into the equation:
8 +
= 1660 - 60
8 +
= 1600
Dividing the whole equation by 4
2 +
= 400
Solving for
2 = 400 -
= 200 - 0.5
Including the marginal cost of firm 1 and multiplying the whole equation by
P = 1660 - 4 - 4
Let's suppose new equation is Y
Y = 1660 - 4
-4
- 60
Pugging in the value of
Y = 1660 - 4
(200 - 0.5
) -4
- 60
Y = 1660 - 800
+2
-4
- 60
Y = 1600 - 800
-2
Taking the derivative w.r.t
= 1600 - 800 - 4
= 0
Solving for
4 = 800
= 200
= 200 - 0.5
Plugging in the value of to get the value of
= 200 - 0.5 (200)
= 200 - 100
= 100
Q = +
Q = 100 + 200
Q = 300
Hence, in equilibrium, total output by the two firms will be option
e= 300.