My computer has a mass of 0.031080997078386 slug the Earth's surface.

Find E[x] when x is sum of two fair dice?

Ksenya-84 [330]

Answer:

When two fair dice are rolled, 6×6=36 observations are obtained.

P(X=2)=P(1,1)=

36

1

P(X=3)=P(1,2)+P(2,1)=

36

2

=

18

1

P(X=4)=P(1,3)+P(2,2)+P(3,1)=

36

3

=

12

1

P(X=5)=P(1,4)+P(2,3)+P(3,2)+P(4,1)=

36

4

=

9

1

P(X=6)=P(1,5)+P(2,4)+P(3,3)+P(4,2)+P(5,1)=

36

5

P(X=7)=P(1,6)+P(2,5)+P(3,4)+P(4,3)+P(5,2)+P(6,1)=

36

6

=

6

1

P(X=8)=P(2,6)+P(3,5)+P(4,4)+P(5,3)+P(6,2)=

36

5

P(X=9)=P(3,6)+P(4,5)+P(5,4)+P(6,3)=

36

4

=

9

1

P(X=10)=P(4,6)+P(5,5)+P(6,4)=

36

3

=

12

1

P(X=11)=P(5,6)+P(6,5)=

36

2

=

18

1

P(X=12)=P(6,6)=

36

1

Therefore, the required probability distribution is as follows.

Then, E(X)=∑X

i

⋅P(X

i

)

=2×

36

1

+3×

18

1

+4×

12

1

+5×

9

1

+6×

36

5

+7×

6

1

+8×

36

5

+9×

9

1

+10×

12

1

+11×

18

1

+12×

36

1

=

18

1

+

6

1

+

3

1

+

9

5

+

6

5

+

6

7

+

9

10

+1+

6

5

+

18

11

+

3

1

=7

E(X

2

)=∑X

i

2

⋅P(X

i

)

=4×

36

1

+9×

18

1

+16×

12

1

+25×

9

1

+36×

36

5

+49×

6

1

+64×

36

5

+81×

9

1

+100×

12

1

+121×

18

1

+144×

36

1

=

9

1

+

2

1

+

3

4

+

9

25

+5+

6

49

+

9

80

+9+

3

25

+

18

121

+4

=

18

987

=

6

329

=54.833

Then, Var(X)=E(X

2

)−[E(X)]

2

=54.833−(7)

2

=54.833−49

=5.833

∴ Standard deviation =

Var(X)

=

5.833

=2.415

4 0

3 years ago

Please help i am give brainliest i really need help guys no links please ???

devlian [24]

Explanation:

The wind is an actual form of solar energy. winds are caused by the heating of the atmosphere by the sun, the rotation of the earth, and the earth's surface irregularities. The wind is capture in a wind turbine which provides a renewable energy source, the wind makes the rotor spin, as the rotor spins the movement of the blades drives a generator that creates energy, also known as wind power. The average wind efficiency of turbines is between 35-45%.

Advantages of wind power

- Wind power is cost-effective

- wind creates jobs

- wind enables US industry growth and US competitiveness

-it's a clean fuel source

4 0

3 years ago

What color is an orange? its for my 8th grade

Ksenya-84 [330]

Answer:

hmmmm i think orange I may be wrong....

Explanation:

5 0

3 years ago

A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls

Inessa05 [86]

Answer:

the percent increase in the velocity of air is 25.65%

Explanation:

Hello!

The first thing we must consider to solve this problem is the continuity equation that states that the amount of mass flow that enters a system is the same as what should come out.

m1=m2

Now remember that mass flow is given by the product of density, cross-sectional area and velocity

(α1)(V1)(A1)=(α2)(V2)(A2)

where

α=density

V=velocity

A=area

Now we can assume that the input and output areas are equal

(α1)(V1)=(α2)(V2)

$\frac{V2}{V1} =\frac{\alpha1 }{\alpha 2}$

Now we can use the equation that defines the percentage of increase, in this case for speed

$i=(\frac{V2}{V1} -1) 100$

Now we use the equation obtained in the previous step, and replace values

$i=(\frac{\alpha1 }{\alpha 2} -1) 100\\i=(\frac{1.2}{0.955} -1) 100=25.65$

the percent increase in the velocity of air is 25.65%

6 0

3 years ago

A rigid bar pendulum is attached to a cart, which moves along the horizontal plane. The rigid bar has a center of mass at L/2. T

Vikentia [17]

Answer:

See the attached picture for answer.

Explanation:

See the attached picture for explanation.

4 0

3 years ago