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Fynjy0 [20]
3 years ago
9

Andre is reviewing proportional relationships. He wants to practice using a graph that goes through a point so that each X-coord

inate and each Y-coordinate is between 1 and 10.
Mathematics
2 answers:
harkovskaia [24]3 years ago
7 0

Answer:

definition, an arc subtended by a central angle of some given measure has the same measure.

Shkiper50 [21]3 years ago
6 0

Answer:

definition, an arc subtended by a central angle of some given measure has the same measure.

Step-by-step explanation:

Believe Meh What she said it works

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A random variable X with a probability density function () = {^-x > 0
Sliva [168]

The solutions to the questions are

  • The probability that X is between 2 and 4 is 0.314
  • The probability that X exceeds 3 is 0.199
  • The expected value of X is 2
  • The variance of X is 2

<h3>Find the probability that X is between 2 and 4</h3>

The probability density function is given as:

f(x)= xe^ -x for x>0

The probability is represented as:

P(x) = \int\limits^a_b {f(x) \, dx

So, we have:

P(2 < x < 4) = \int\limits^4_2 {xe^{-x} \, dx

Using an integral calculator, we have:

P(2 < x < 4) =-(x + 1)e^{-x} |\limits^4_2

Expand the expression

P(2 < x < 4) =-(4 + 1)e^{-4} +(2 + 1)e^{-2}

Evaluate the expressions

P(2 < x < 4) =-0.092 +0.406

Evaluate the sum

P(2 < x < 4) = 0.314

Hence, the probability that X is between 2 and 4 is 0.314

<h3>Find the probability that the value of X exceeds 3</h3>

This is represented as:

P(x > 3) = \int\limits^{\infty}_3 {xe^{-x} \, dx

Using an integral calculator, we have:

P(x > 3) =-(x + 1)e^{-x} |\limits^{\infty}_3

Expand the expression

P(x > 3) =-(\infty + 1)e^{-\infty}+(3+ 1)e^{-3}

Evaluate the expressions

P(x > 3) =0 + 0.199

Evaluate the sum

P(x > 3) = 0.199

Hence, the probability that X exceeds 3 is 0.199

<h3>Find the expected value of X</h3>

This is calculated as:

E(x) = \int\limits^a_b {x * f(x) \, dx

So, we have:

E(x) = \int\limits^{\infty}_0 {x * xe^{-x} \, dx

This gives

E(x) = \int\limits^{\infty}_0 {x^2e^{-x} \, dx

Using an integral calculator, we have:

E(x) = -(x^2+2x+2)e^{-x}|\limits^{\infty}_0

Expand the expression

E(x) = -(\infty^2+2(\infty)+2)e^{-\infty} +(0^2+2(0)+2)e^{0}

Evaluate the expressions

E(x) = 0 + 2

Evaluate

E(x) = 2

Hence, the expected value of X is 2

<h3>Find the Variance of X</h3>

This is calculated as:

V(x) = E(x^2) - (E(x))^2

Where:

E(x^2) = \int\limits^{\infty}_0 {x^2 * xe^{-x} \, dx

This gives

E(x^2) = \int\limits^{\infty}_0 {x^3e^{-x} \, dx

Using an integral calculator, we have:

E(x^2) = -(x^3+3x^2 +6x+6)e^{-x}|\limits^{\infty}_0

Expand the expression

E(x^2) = -((\infty)^3+3(\infty)^2 +6(\infty)+6)e^{-\infty} +((0)^3+3(0)^2 +6(0)+6)e^{0}

Evaluate the expressions

E(x^2) = -0 + 6

This gives

E(x^2) = 6

Recall that:

V(x) = E(x^2) - (E(x))^2

So, we have:

V(x) = 6 - 2^2

Evaluate

V(x) = 2

Hence, the variance of X is 2

Read more about probability density function at:

brainly.com/question/15318348

#SPJ1

<u>Complete question</u>

A random variable X with a probability density function f(x)= xe^ -x for x>0\\ 0& else

a. Find the probability that X is between 2 and 4

b. Find the probability that the value of X exceeds 3

c. Find the expected value of X

d. Find the Variance of X

7 0
2 years ago
Which of these points does not change its location when it is reflected across the y-axis? (2, 0) (0, 6) (3, 3) (–5, 5)
Anna [14]

Answer:

-5,5

Step-by-step explanation:

5 0
3 years ago
Nancy walks 5 blocks to the right , 3 blocks down , 7 blocks to the left and 1 block up each square size length is 1 block. What
Lelu [443]
I really dont know how to explain it but its (-2,-2)
7 0
2 years ago
Read 2 more answers
At sunrise the temperature in Anchorage was -4°F. By 2pm the
Ainat [17]
The answer is 19 degrees F.

15 - (-4) = 19
6 0
3 years ago
Tell whether (4, 27) is a solution of y=3x+15
Brilliant_brown [7]

Answer:

Yes

Step-by-step explanation:

We have two properties for our question :

(4, 27)

y = 3x + 15

We are being asked whether the point (4, 27) is a solution of y = 3x + 15

So how do we figure this out? Well, what we have to know first that (4, 27)  represents a variable, 4 which is the run on the graph, represents x in a solution. And 27 which is the rise on the graph, represents y in the solution. So when asking for a solution with two points, all we must do is substitute x and y for the two coordinates.

y = 3x + 15

y = 27 and x = 4

27 = 3(4) + 15

27 = 12 + 15

27 = 27

Since this equation is true with the respected variables, therefore signifies that (4,27) is a solution of y = 3x + 15

5 0
2 years ago
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