Hi, can anyone draw me an isometric image of this shape?

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

2 years ago

Which term represents an object that has a round or oval base and is connected at every point by lines at a corresponding point

raketka [301]

Answer:

it is a polyhedron

Explanation:

if I am wrong I am sorry

8 0

3 years ago

Read 2 more answers

The total solids production rate in an activated sludge aeration tank is 7240 kg/d on a dry mass basis. It is necessary to maint

snow_lady [41]

Answer:

volume of biological sludge = 28.566 m³ per day

Explanation:

given data

mass of solid = 7240 kg/day

initial moisture content = 78%

solution

here percentage of solid will be

% of solid = 100 - initial moisture content

% of solid = 100 - 78 = 22 %

so that

mass of sludge produced = $\frac{100}{100 - P} M$ kg per day

put her value

mass of sludge produced = $\frac{100}{100 - 78} 7240$ kg

mass of sludge produced = 32909.09 kg

so

specific gravity of sludge = $\frac{\rho sludge}{\rho water }$

and as we know that

$\frac{100}{S sludge} = \frac{solid percentage}{S solid} = \frac{water percentage}{S water}$

$\frac{100}{S sludge} = \frac{22}{2.5} = \frac{78}{1}$

$S sludge$ = 1.152

so that

density of sludge = S sludge × density of water

density of sludge = 1.152 × 1000

density of sludge = 1152 kg/m³

so that

volume of biological sludge = $\frac{mass sludge produce}{\rho sludge}$

volume of biological sludge = $\frac{32909.09}{1152}$

volume of biological sludge = 28.566 m³ per day

6 0

3 years ago

Determine the work done by an engine shaft rotating at 2500 rpm delivering an output torque of 4.5 N.m over a period of 30 secon

balu736 [363]

Answer:

work done= 2.12 kJ

Explanation:

Given

N=2500 rpm

T=4.5 N.m

Period ,t= 30 s

$torque =\frac{power}{2\pi N}$

$power=2\pi N\times T$

P= $2\times \pi \times2500 \times 4.5$

P=70,685W

P=70.685 KW

power= $\frac{work done}{time}$

work done = power * time

= 70.685*30=2120.55J

= 2.12 kJ

7 0

3 years ago

How can I solve 23.5 million Nona meters to millimeters using no calculator because I have to show my work

lozanna [386]

Answer:

its so simple. u must mind some formulas.

Explanation:

mili->10^(-3)

micro->10^(-6)

nano->10^(-9)

so write the exact number and move "." to left or right depend question.

in this one:

23.5 is 23500000.0 nano with a default dot at the end

for turning to mili u must move the dot 6 steps to left so it will be: 23.5 milimeter.

6 0

3 years ago

Hi, can anyone draw me an isometric image of this shape?​

Hi, can anyone draw me an isometric image of this shape?