The swimming pool is open when the high temperature is higher than 20°C. Lainey tried to swim on

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

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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)

8 0

1 year ago

(729x^3y^20z^11)^1/5

s2008m [1.1K]

Answer:

729/5 • x^3 • y^20 • z^11

Step-by-step explanation:

7 0

3 years ago

50 pts-----Is there a special way to solve a question like this (without calculator)

andreyandreev [35.5K]

The only way to do it is 1.8x1.8x1.8x1.8x1.8x1.8x1.8x1.8x1.8. Or just use a calculator. Sorry to let you down

4 0

3 years ago

Which equation is equivalent to 3x – 4y = 8?

lawyer [7]

The answer is <span>D) Y = 3/4x-2
</span>
3x - 4y = 8
Express it in the term of y.

Subtract 3x from both sides:
3x - 4y - 3x = 8 - 3x
- 4y = 8 - 3x

Divide both sides by -4
-4y/-4 = (8 - 3x)-4
y = 8/-4 - 3x/-4
y = -2 - (-3/4x)
y = -2 + 3/4x
y = 3/4x - 2

4 0

3 years ago

I need help please! Thank you

Debora [2.8K]

Answer:

We also know that If two angles are complementary then their sum is equal to 90°. So, two angles ∠1 & ∠2 are complementary.

Step-by-step explanation:

As BA is perpendicular to BC. So, angle ∠ABC is 90°.

We also know that If two angles are complementary then their sum is equal to 90°. As ∠ABC is the sum of the ∠1 & ∠2. In other words, ∠1 & ∠2 are complementary. So, two angles ∠1 & ∠2 are complementary.

Lets prove this.

Given: BA ⊥ BC

Prove: ∠1 & ∠2 are complementary.

Statement Reasons

1. ∠1 & ∠2 are complementary 1. Given

2. ∠1 + ∠2 = 90° 2. Def. of complementary angles

7 0

3 years ago