Mathematics College

Suppose that X is a random variable with mean 20 and standard deviation 5. Also suppose that Y is a random variable with mean 40 and standard deviation 10. Assume that the correlation between X and Y is 0.5. Find the mean and variance of the random variable Z = ????3X ???? 2Y . Be sure to show all your work.

Answers

Answer 1

Answer:

[tex]E(Z) = 202 [/tex]

[tex]E(Z) = 198[/tex]

[tex]E(Z) = -140 [/tex]

Step-by-step explanation:

From the question we are told that

The mean of X is [tex] E(X) = 20[/tex]

The standard deviation of X is [tex]s_1 = 5[/tex]

The mean of Y is [tex]\= y = 40[/tex]

The standard deviation of Y is [tex]s_2 = 10[/tex]

Considering question a

Generally the mean of Z = 2 + 10X. is mathematically represented

[tex]E(Z) = E[2 + 10X ][/tex]

=> [tex]E(Z) = 2 + 10 E(X)[/tex]

=> [tex]E(Z) = 2 + 10 * 20 [/tex]

=> [tex]E(Z) = 202 [/tex]

Considering question b

Generally the mean of Z = 10X - 2.. is mathematically represented

[tex]E(Z) = E[10X -2 ][/tex]

=> [tex]E(Z) = 10E(X) - 2[/tex]

=> [tex]E(Z) = 10* 20 - 2[/tex]

=> [tex]E(Z) = 200 - 2[/tex]

=> [tex]E(Z) = 198[/tex]

Considering question c

Generally the mean of -3X - 2Y is mathematically represented

[tex]E(Z) = E[-3X -2Y ][/tex]

[tex]E(Z) = -3 E(X) -2E(Y) [/tex]

=> [tex]E(Z) = -3 * 20 -2* 40 [/tex]

=> [tex]E(Z) = -140 [/tex]

Suppose That X Is A Random Variable With Mean 20 And Standard Deviation 5. Also Suppose That Y Is A Random

Related Questions

Solve x2 - 4x + 1 = 0.
x= 2 + 2i15
x = 4+ V3
x = 2/3
x= -2-3

Answers

Answer:

x = 2 ± √ 3

Step-by-step explanation:

The sum of three times a number and seven is 22

Answers

Answer:

3x+7=22

Step-by-step explanation:

three times a number is

[tex]3\times x=3x[/tex]

so the sum of 3x and 7 is 22

[tex]3x+7=22\\\\3x=15\\\\x=5[/tex]

you can leave it here

[tex]3x+7=22[/tex]

if you need the value of x

then

[tex]x=5[/tex]

What kind of lines are shown?

Answers

Answer:

vertical and horizontal

Which of the following expressions is equal to 4+3(x-2)?

Answers

Answer:

i believe it is "3x+2"

Explanation:

first you distribute the 3 to the expression in the parenthesis and you get "3x-6" and add the +4 to the end of that expression and you get "3x-6+4" add "-6+4" and you get "-2" and then you get "3x--2"since a subtraction sign and a negative sign make it be addition you get the expression "3x+2"

i think the answer is 3x + 2

Question Help When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 36 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 3000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

Answers

Answer:

The probability is [tex]P(X \le 2 ) = 0.9072[/tex]

The company will accept 90.72% of the shipment and will reject [tex](100 -90.72) = 9.2\%[/tex] of the shipment , so many of the shipment are rejected

Step-by-step explanation:

From the question we are told that

The sample size is n = 36

The proportion that did not meet the requirement is [tex]p = 0.03[/tex]

Generally the probability that the whole shipment is accepted is equivalent to the probability that there is at most 2 batteries that do not meet the requirement , this is mathematically represented as

[tex]P(X \le 2 ) = [ P(X = 0 ) + P(X = 1 ) + P(X = 0)][/tex]

=> [tex]P(X \le 2 ) = [ [^{n}C_0 * (p)^{0} *(1-p)^{n-0} ] + [^{n}C_1 * (p)^{1} *(1-p)^{n-1} ] + [^{n}C_2 * (p)^{2} *(1-p)^{n-2} ]][/tex]

Here C stands for Combination (so we will be making the combination function in our calculators )

=> [tex]P(X \le 2 ) = [ [^{36}C_0 * (0.03)^{0} *(1-0.03)^{36-0} ] + [^{36}C_1 * (0.03)^{1} *(1-0.03)^{36-1} ] + [^{36}C_2 * (0.03)^{2} *(1-0.03)^{36-2} ]][/tex]

=> [tex]P(X \le 2 ) = [ [1 * 1 * 0.3340 ] + [36* 0.03 *0.3444 ] + [630 * 0.0009 *(0.355 ]][/tex]

=>[tex]P(X \le 2 ) = 0.9072[/tex]

The company will accept 90.72% of the shipment and will reject [tex](100 -90.72) = 9.2\%[/tex] of the shipment , so many of the shipment are rejected

Rachel estimates the weight of her dog to be 50 pounds the actual weight of the dog is 52.5 pounds what is the percent error of Rachel’s estimate

Answers

Answer:

It is unidentified.

Step-by-step explanation:

3x - 5 = 2x + 10
What’s the value of x

Answers

Answer:

x = 3

Step-by-step explanation:

braniest pls

Answer:

x=3

Step-by-step explanation:

-5 +10

+5=15

+5=0

3x, 2x

+2 -2

5x=15

_ _

x=3

Evaluate the following expression,
5x [7+ (10-2) + 4)

Answers

Answer: 95x

Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)

Add 7 and 10.

5x(17-2+4)

Add 15 and 4.

5x multiped by 19

Multiply 19 by 5

95x

You are buying fruit to make fruit baskets. Apples come in bags of 20. Oranges come in bags of 16, and bananas come in bags of 32. You have one bag of each fruit. Each fruit basket must be identical. What is the greatest number of fruit baskets that you can make using all of the fruit? *

Answers

Answer:

4 fruit baskets.

Step-by-step explanation:

Use GCF to find the answer. 20 divided by 4 is 5, 16 divided by 4 is 4, and 32 divided by 4 is 8.

Playing golf, Mike got a + 2on the first hole and - 2 on the second hole. What is his combined score for the first two holes?

Answers

Answer:

Step-by-step explanation:

he had a score of 2 on the first hole and then he go a birdie i think and it subtracted 2 from that leaving 0

"The intersection of two planes is a line" is a statement that is generally accepted as true, but
cannot be proven to be true. What type of statement is this?
1. defined
2. undefined
3. postulate
4. proof

Answers

Answer: 3. Postulate

A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.

Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change. What is the probability that the time until the next change is greater than 9.5 days

Answers

Answer:

The probability will be "0.205".

Step-by-step explanation:

The probability that perhaps the time remains greater than 9.5 days before the next shift will indeed be:

⇒ [tex]P(X>9.5)[/tex]

⇒ [tex]1-P(X<9.5)[/tex]

⇒ [tex]1-(1-exp(\frac{-9.5}{6} ))[/tex]

⇒ [tex]0.205[/tex]

PLEASE HELP
For spirit week at a local high school, students were encouraged to wear their school colors of green and white. 1,200 students wore their school colors while 300 students did not wear green and white. What percent of the school population did NOT wear their school colors?
Here are the answer choices

A.
15%

B.
20%

C.
25%

D.
33%

Answers

Answer:

C. 25% The correct answer is C. 300 divided by 1200 equals 25%.

Step-by-step explanation:

Answer:

B.) 20%

Step-by-step explanation:

First, add 1,200 and 300. That gives you 1,500. You want to find how much percent of 1,500 equals 300, and that is 20%.

Which of the following is a true statement about the triangles shown on the graph?

The slope of the smaller triangle is smaller than the slope of the larger triangle
The slope of the larger triangle is larger than the slope of the smaller triangle.
The triangles are congruent triangles.
The slopes of the two triangles are the same.

Answers

The correct statement about the triangles shown in the graph is given as follows:

The slopes of the two triangles are the same.

How to obtain the slope?

Considering a graph, a slope is calculated as the division of the vertical change by the horizontal change.

For the smaller triangle, we have that:

The vertical change is of 2.The horizontal change is of 2.

Hence the slope is of:

m = 2/2

m = 1.

For the larger triangle, we have that:

The vertical change is of 3.The horizontal change is of 3.

Hence the slope is of:

m = 3/3.

m = 1.

Meaning that they have the same slope.

More can be learned about slope at https://brainly.com/question/24808124

#SPJ1

What is the value of sin-1(1)?

Answers

The value of sin^(-1) 1 is; π/2

We want to find the value of sin^(-1) 1

Answer:

hshshshshshshshsiqkZjfdudiodjfhfbbxdudijdd

Toni is shopping for clothes at the store she buys 8 shirts for $8.00 what is the unit rate for the shirts?

Answers

Answer:

$1.00

Step-by-step explanation:

The unit rate in this scenario would be $1.00 , meaning that Toni is paying $1.00 for every shirt. This can be calculated by dividing the total price that she is paying for the shirts by the total number of shirts that Toni is purchasing like so...

$8.00 / 8 = $1.00 per shirt

The unit rate is basically the value over the denominator of 1 which would be the case as seen above since $1 buys 1 shirt ([tex]\frac{1 dollar}{1 shirt}[/tex]) as opposed to $8 dollars 8 shirts ([tex]\frac{8 dollars}{8 shirts}[/tex]) as mentioned in the question.

The set A = {1, 3, 5}. What is a larger set this might be a subset of?

Answers

Answer:

Step-by-step explanation:

A larger set that a particular set can be a subset of is a Universal set. A universal set is parent where all other sets are derived from.

For example, given a universal set U = {1,2,3,4,5}, a set A = {1, 3, 5} is said to be a subset of the set U because the elements of set B are contained in the Universal set U.

Also, sets like {1, 4,5} and {3,4,5} can also be regarded as the subset of U since all the elements of the sets can be found in the Universal set U. Hence the correct name of the set is a UNIVERSAL SET

So, the number of maximum subsets we can create from the given set is 8.

Subsets:

The subsets of any set consists of all possible sets including its elements and the null set. Let us understand with the help of an example.

Example: Find all the subsets of set A = {1,2,3,4}

Solution: Given, A = {1,2,3,4}

Subsets =

The subsets of any set consisting of all possible sets including its elements and the null set. Let us understand with the help of an example.

Example: Find all the subsets of set A = {1,2,3,4}

{}

{1}, {2}, {3}, {4},

{1,2}, {1,3}, {1,4}, {2,3},{2,4}, {3,4},

{1,2,3}, {2,3,4}, {1,3,4}, {1,2,4}

{1,2,3,4}

So, the formula is [tex]2^n[/tex].

The given set is,

[tex]A = \{1, 3, 5\}[/tex]

Here the number of an element is 3.

So, the maximum number of subsets we can create is,

[tex]2^n=2^3=8[/tex]

Learn more about the topic Subsets:

https://brainly.com/question/17514113

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