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2 years ago

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

Engineering

1 answer:

Ksenya-84 [330]2 years ago

4 0

Answer:

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

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

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

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

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

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

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

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

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

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

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

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

Therefore, the required probability distribution is as follows.

Then, E(X)=∑X

⋅P(X

)

=2×

+3×

+4×

+5×

+6×

+7×

+8×

+9×

+10×

+11×

+12×

+1+

E(X

)=∑X

⋅P(X

)

=4×

+9×

+16×

+25×

+36×

+49×

+64×

+81×

+100×

+121×

+144×

+5+

+9+

121

987

329

=54.833

Then, Var(X)=E(X

)−[E(X)]

=54.833−(7)

=54.833−49

=5.833

∴ Standard deviation =

Var(X)

5.833

=2.415

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A fluid flows steadily through a pipe with a uniform cross sectional area. The density of the fluid decreases to half its initia

Vikentia [17]

Answer:

c. V2 equals V1

Explanation:

We can answer this question by using the continuity equation, which states that:

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where

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A2 is the cross-sectional area in the second section of the pipe

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v2 is the velocity of the fluid in the second section of the pipe

In this problem, we are told that the pipe has a uniform cross sectional area, so:

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As a consequence, according to eq.(1), this means that

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2 years ago

Why do engineers play a variety of roles in the engineering process?

Crazy boy [7]

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Explanation:

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2 years ago

Single point cutting tool removes material from a rotating work piece to generate a cylinder is called • Facing Tuming • Both 1

madam [21]

Answer:Turning

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A fluid of specific gravity 0.96 flows steadily in a long, vertical 0.71-in.-diameter pipe with an average velocity of 0.90 ft/s

KengaRu [80]

Answer:

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Explanation:

diameter ( D ) = 0.71 inches = 0.0591 ft

velocity = 0.90 ft/s ( V )

fluid specific gravity = 0.96 (62.4 ) ( x )

change in pressure ( P ) = 0 because pressure was constant

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= ( 0 - 0.96( 62.4) sin -90 ) * 0.0591 ^2 / 32 * 0.90

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8 0

3 years ago

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