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Nana76 [90]
4 years ago
15

Evaluate 3x^2-1 when x=2

Mathematics
2 answers:
Artemon [7]4 years ago
6 0
Hey there,

3x^2 - 1 (x = 2)

Plug in 2 for x

3(2)^2 - 1

Do the exponent

3(4) -1

Multiply and the subtract

12 -1 = 11

The answer would be 11

Hope I helped :)

~Char
AlekseyPX4 years ago
3 0
3x^2-1, x=2

3(2)^2-1

3(4)-1

12-1

11

When x=2, 3x^2-1=11.
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X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y
andriy [413]

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

<h3>What is normal random variables?</h3>

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}

Part b.

Consider V(3X + 2Y)

\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

3 X+2 Y \sim N(18,77)

Thus,

P(3 X+2 Y < 18)=0.5

Part d.

Consider P(3X + 2Y < 28)

Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}

\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

brainly.com/question/23836881

#SPJ4

The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

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Explain why 2+x and x+3 are equivalent
wlad13 [49]

Check whether the two expressions 2x+3y2x+3y and 2y+3x2y+3x equivalent.

The first expression is the sum of 2x2x 's and 3y3y 's whereas the second one is the sum of 3x3x 's and 2y2y 's.

Let us evaluate the expressions for some values of xx and yy . Take x=0x=0 and y=1y=1 .

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Nat2105 [25]
Answer:
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