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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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Step-by-step explanation:

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1. Consider f(x) = 3x - 5
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Answer:

3

Step-by-step explanation:

Here we have the function

f(x)=3x-5

We want to find the following ratio:

\frac{f(x+h)-f(x)}{h}

Note that the limit of this for h\rightarrow 0 is equivalent to the derivative of the function.

Here we have:

f(x+h)=3(x+h)-5=3x+3h-5

And

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f(x+h)-f(x)=3x+3h-5-(3x-5)=3h

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Give an example of an event that is certain and an event that is impossible. What are the probabilities for each event?
OleMash [197]

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Thank you for posting your question here at brainly. Feel free to ask more questions.  

The best and most correct answer among the choices provided by the question is 0 (zero).          

Hope my answer would be a great help for you.  3 to all sorry i can't help you all i try my best tho my goal is to get to 4 brainlyest may 8 if i'm lucky god bless you all stay safe during these tuff times

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2 years ago
Read 2 more answers
Jake is solving x^2-6x+5=0 by completing the square his steps are shown below step 1. x^2-6x=-5 step 2. x^-6x+9=-5+9 step 3. (x-
damaskus [11]

Answer:

Jake's error in step 3

Step-by-step explanation:

we have

x^{2} -6x+5=0

Complete the square

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2} -6x=-5

step 2

Complete the square. Remember to balance the equation by adding the same constants to each side

x^{2} -6x+9=-5+9

x^{2} -6x+9=4

step 3

Rewrite as perfect squares

(x-3)^{2}=4

Jake's error in step 3

He placed 6 instead of 3 in the left side

step 4

take square root both sides

\sqrt{(x-3)^2} =\sqrt{4}

step 5

(x-3)=\pm2

step 6

x=3\pm2

step 7

x=5 and x=1

7 0
3 years ago
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