Use the Law of Syllogism to form a new conditional statement that follows from the pair of true statements.

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

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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

2 years ago

Determine the point estimate of the population proportion and the margin of error for the following confidence interval.Lower bo

Kamila [148]

Answer: The point estimate of the population proportion is . 485.

The margin of error is 0.273.

Step-by-step explanation:

Confidence interval for population proportion(p):

sample proportion ± Margin of error

Given: Lower bound of confidence interval = 0.212

Upper bound = 0.758

⇒sample proportion - Margin of error=0.212 (i)

sample proportion + Margin of error= 0.758 (ii)

Adding (i) and (ii) , we get

2(sample proportion) =0.970

⇒ sample proportion = 0.970÷2= 0.485

Since sample proportion is the point estimate of the population proportion.

So, the point estimate of the population proportion= 0.485

Now put sample proportion =0.485 in (ii), we get

0.485+ Margin of error= 0.758

⇒ Margin of error= 0.758 - 0.485 =0.273

i.e. The margin of error is 0.273.

5 0

3 years ago

Max has 5 red model cars. One third of his model cars are red. How many model cars does Max have?

Ber [7]

5=red
1/3 of all=red
1/3 of all=5
3/3 of all=all=1/3 times 3/1=5 times 3/1=15

15 total

6 0

3 years ago

Read 2 more answers

The temperature is -13°F. A high pressure front increases the temperature to 18°F. By how much degrees did the temperature incre

blsea [12.9K]

The difference between the 2 different temperatures.
The key word difference refers to subtraction.
So 18 - ( - 13 )
Subtracting a negative is the same as adding the positive.
So 18 + 13
Solve the statement to get:
31

8 0

3 years ago

Evaluate the sum of the finite geometric series.

Dmitry [639]

Answer:

descarga la aplicación photomath

4 0

3 years ago