1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arte-miy333 [17]
3 years ago
7

HELP PLEASE!!! The expected value of a random variable X is 35. The variable is transformed

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
7 0

Answer:

Expected value x= 35

linear transformation is defined as a + bx

here, b=4, a=1

The transformation is z=1+4x

now, expected value, l_z=l_z(a+bx)

=l(a)+l(bx)

=a+b\:l\:x

substitute the value of a=1, b=4 and l=35

l_z=1+4\times35

=1+140

=141

So, the expected value of the transformed variable is <u>141</u>.

<u>OAmalOHopeO</u>

sdas [7]3 years ago
5 0
<h3>Answer:  D) 141</h3>

=======================================================

Explanation:

Let's consider a set of three values such that they're all equal to 35

{35,35,35}

This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.

If we multiply everything by 4, then we get the new set {140,140,140}

Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.

-----------------------------

You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.

If we quadruple each item, then we have {34,35,36} turn into {136,140,144}

Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.

These are just two examples you could do to help see why the answer is D) 141

-----------------------------

In a more general theoretical sense, we're saying the following

Y = mX+b

E[Y] = E[m*X+b]

E[Y] = E[m*X] + E[b]

E[Y] = m*E[X] + b

where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.

So,

E[Y] = m*E[X] + b

E[Y] = 4*35 + 1

E[Y] = 141

-----------------------------

Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.

A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.

You might be interested in
how many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/3 inc
borishaifa [10]
Volume of one cubic block = (1/6)^3  = 1/216 cu ins

Volume of the prism = 1/3 * 2/3 * 2/3  = 4/27  cu ins

Number of blocks to fill prism  = 4/27 / 1/216   = (216*4) / 27  =  32
3 0
3 years ago
Read 2 more answers
A computer online service charges one hourly rate for regular use but a higher hourly rate for designated "premium" areas. One c
N76 [4]

Answer: the service charge per hour for premium services is $5.5

the service charge per hour for regular services is $3

Step-by-step explanation:

Let x represent the service charge per hour for premium services.

Let y represent the service charge per hour for regular services.

One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that

2x + 9y = 38- - - - - - - - - - - 1

Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that

3x + 6y = 34.5- - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes

6x + 27y = 114

6x + 12y = 69

Subtracting, it becomes

15y = 45

y = 45/15

y = 3

Substituting y = 3 into equation 1, it becomes

2x + 9 × 3 = 38

2x + 27 = 38

2x = 38 - 27 = 11

x = 11/2 = 5.5

8 0
3 years ago
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
katrin [286]

Answer:

the answer is b bro

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Create your own real-world example of a relation that is a function. Domain: The set of Range: The set of
ivanzaharov [21]

Answer:

C(t)=5000 -10t

Step-by-step explanation:

There are many examples in the real world of relationships that are functions.

For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.

If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:

C(t)=C_{0}-at\\

Where:

C (t): Amount of water in the tank as a function of time

C_{0}: Initial amount of water in the tank at time t = 0

a: amount of water lost per hour

t: time in hours

Then the equation is:

C(t)=5000 -10t

The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.

Its domain is the set of all positive real numbers t between [0,500]

Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty

Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres

7 0
3 years ago
Read 2 more answers
What is 8/24 subtracting 1 quart
posledela
The answer to your math problem is0.083333
5 0
3 years ago
Read 2 more answers
Other questions:
  • Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer a
    6·1 answer
  • Seed are often treated with fungicides to protect them in poor draining, wet environments. A small-scale trial, involving five t
    14·1 answer
  • What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5
    12·2 answers
  • What Is the perimeter of a=4 and b=2????
    9·2 answers
  • A ball is dropped from the top of a building that is 492 feet high. Use the formula below to find height of the ball 2 seconds a
    5·1 answer
  • Are 4e and 4 like or unlike? *
    10·2 answers
  • Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many
    6·1 answer
  • 8) Solve: X + 250 = 700
    12·1 answer
  • Find (fog)(-3).<br> f(x) = x + 5<br> g(x) = x2 + 1<br> (fog)(-3) =<br> Submit
    11·1 answer
  • Subject
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!