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boyakko [2]
3 years ago
13

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X . What are the mean and s

tandard deviation of W ?
Mathematics
2 answers:
patriot [66]3 years ago
6 0

Answer:

The mean and standard devaition of W are 6 and 31 respectively.

Step-by-step explanation:

Given that:

W = 7 + 2X

Variance (W) = Variance(7 + 2X)

For a term constant term, the variance is zero.

So;

W = Var (2X)

W = 4 × Var(X)

W = 4 × (SD (X))²

W = 4 × (3)²

W = 4 × 9

W = 36

Thus, Variance (W) = 36

The standard deviation of W = \sqrt{variance}

W = \sqrt{36}

W = 6

Also;

E(W) = E(7 +2 X)

E(W) = 7 + 2 × E(X)

where;

mean X = 12

E(W) = 7 + 2(12)

E(W) = 31

Thus, the mean and standard devaition of W are 6 and 31 respectively.

Ivan3 years ago
4 0

Answer:

The mean is 31, and the standard deviation is 6.

Step-by-step explanation:

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For any number n>1, is |(0.8 + 0.8i)| a. Greater than 1? b. Less than 1? c. Equal to 1?​
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5 0
2 years ago
The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+
jekas [21]

Answer:

Total revenue = \frac{169}{2}\ln(13)-\frac{169}{4}  dollars

Step-by-step explanation:

R'(x)=(x+1)\ln(x+1)

Integrate with respect to x.

R(x)= ∫(x+1)\ln(x+1) dx

Take x+1=u

Differentiate with respect to x

dx=du

So,

R(x)= ∫u\ln(u)\,du

Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx

Therefore,

R(x)=  \frac{u^2}{2}\ln(u) -  ∫\frac{u^2}{2}\frac{1}{u}\,du

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Put u=x+1

R(x)=   \frac{(x+1)^2}{2}\ln(x+1)-\frac{(x+1)^2}{4}

To find total revenue from the sale of the first 12 calculators, put x=12

R(x)=   \frac{(12+1)^2}{2}\ln(12+1)-\frac{(12+1)^2}{4}\\\\= \frac{(13)^2}{2}\ln(13)-\frac{(13)^2}{4}\\\\=\frac{169}{2}\ln(13)-\frac{169}{4}

Total revenue = \frac{169}{2}\ln(13)-\frac{169}{4}  dollars

4 0
3 years ago
A movie theater sold 2,604 tickets in 6 days. they sold the same number of tickets each day. How many tickets did the theater se
puteri [66]

Answer: The movie theater sold 434 a day

Step-by-step explanation:

How I got 434 a day

So

If you multiply 434 x 6 = 2,604

so they sold 2,604 in 6 days.

Let me know if I did something wrong.

5 0
3 years ago
I need help with this problem
rewona [7]
I believe the answer is A

6 0
3 years ago
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