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Nat2105 [25]
3 years ago
7

Suppose that X1 and X2 are independent random variables each with a mean μ and a variance σ^2. Compute the mean and variance of

Y = 3X1 + X2.
Mathematics
1 answer:
Deffense [45]3 years ago
5 0

Mean:

E[Y] = E[3X₁ + X₂]

E[Y] = 3 E[X₁] + E[X₂]

E[Y] = 3µ + µ

E[Y] = 4µ

Variance:

Var[Y] = Var[3X₁ + X₂]

Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]

(the covariance is 0 since X₁ and X₂ are independent)

Var[Y] = 9 Var[X₁] + Var[X₂]

Var[Y] = 9σ² + σ²

Var[Y] = 10σ²

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The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management
dexar [7]

Answer:

d. 15

Step-by-step explanation:

Putting the values in the shift 2 function

X1 + X2 ≥ 15

where x1=  13, and x2=2

13+12≥ 15

15≥ 15

At least 15 workers must be assigned to the shift 2.

The LP model questions require that the constraints are satisfied.

The constraint for the shift 2 is that the  number of workers must be equal or greater than 15

This can be solved using other constraint functions e.g

Putting  X4= 0 in

X1 + X4 ≥ 12

gives

X1 ≥ 12

Now Putting the value X1 ≥ 12  in shift 2 constraint

X1 + X2 ≥ 15

12+ 2≥ 15

14 ≥ 15

this does not satisfy the condition so this is wrong.

Now from

X2 + X3 ≥ 16

Putting X3= 14

X2 + 14 ≥ 16

gives

X2  ≥ 2

Putting these in the shift 2

X1 + X2 ≥ 15

13+2 ≥ 15

15 ≥ 15

Which gives the same result as above.

6 0
3 years ago
How to add fractions with different denominators and negative numbers?
Kisachek [45]
Let find the least of common multiple = LCM it’s for the denominators.
Multiple of the numerator then the denominator to get the denominators
Don’t forget to to add the numerator but leave the denominators the same
8 0
3 years ago
patrick drank 3/4 liters of water on wednesday before going jogging and 4/5 liter of water after his jog . how much water did pa
Alona [7]
To find the total of 3/4 and 4/5 is to add them together. However, in order to add them together you need to find the least common denominator (LCD). And the LCD of both denominators would be 20, because that is the smallest number both 4 and 5 can divide into. And here is the tricky part, now you have to change the numerators. So since 3/4th's now has a denominator of 20 you have to make the 3 match the 20. So 4 times what it 20? It is 5. So now multiply 5 by three and that will give you 15/20, which can reduce to 3/4 which means that you did this correctly! Now repeat the same steps with 4/5:

4/5=4/20
20÷5=4
4•4=16
16/20    (16/20 can reduce to 4/5 which means you did this correctly.

Now to add them keep the denominators the same and only add the numerators:

15/20 + 16/20 = 31/20

Now this as a mixed number would be 1 11/20. I hope this was helpful!
4 0
2 years ago
Read 2 more answers
If the ratio of blue marbles to red is 9:4 what is possible number of blue and red marbles in the jar
LuckyWell [14K]

Answer:

13

Step-by-step explanation:

13 right? all ya gotta do is add em together right?

5 0
2 years ago
19) Write the scientific notation of 1
mylen [45]

Answer:

1.0 x 10^0

Step-by-step explanation:

The above works because 10^0 = 1, and 1 x 1 = 1.

Brainliest, please :)

7 0
1 year ago
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