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
GaryK [48]
3 years ago
10

Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodo

logy for Probabilistic Life Prediction of Multiple-Anomaly Materials"(Amer. Inst. of Aeronautics and Astronautics J.,2006:787-793) proposes a Poisson distribution for X. Suppose that µ=4. a. Compute both P(X≤4) and P(X<4). b. Compute P(4≤X≤ 8). c. Compute P(8≤ X). d. What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation?
Mathematics
1 answer:
Shkiper50 [21]3 years ago
4 0

Answer:

a) P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.6288

P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.1954=0.4335

b) P(4\leq X\leq 8)=0.1954+0.1563+0.1042+0.0595+0.0298=0.5452

c) P(X \geq 8) = 1-P(X

d) P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559

Step-by-step explanation:

Let X the random variable that represent the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. We know that X \sim Poisson(\lambda=4)

The probability mass function for the random variable is given by:

f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...

And f(x)=0 for other case.

For this distribution the expected value is the same parameter \lambda

E(X)=\mu =\lambda=4  , Var(X)=\lambda=2, Sd(X)=2

a. Compute both P(X≤4) and P(X<4).

P(X\leq 4)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)+P(X=4)

Using the pmf we can find the individual probabilities like this:

P(X=0)=\frac{e^{-4} 4^0}{0!}=e^{-4}=0.0183

P(X=1)=\frac{e^{-4} 4^1}{1!}=0.0733

P(X=2)=\frac{e^{-4} 4^2}{2!}=0.1465

P(X=3)=\frac{e^{-4} 4^3}{3!}=0.1954

P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954

P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.9646

P(X< 4)=P(X\leq 3)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)

P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.5311=0.7692

b. Compute P(4≤X≤ 8).

P(4\leq X\leq 8)=P(X=4)+P(X=5)+ P(X=6)+P(X=7)+P(X=8)

P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954

P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563

P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042

P(X=7)=\frac{e^{-4} 4^7}{7!}=0.0595

P(X=8)=\frac{e^{-4} 4^8}{8!}=0.0298

P(4\leq X\leq 8)=0.1954+0.1563+ 0.1042+0.0595+0.0298=0.5452

c. Compute P(8≤ X).

P(X \geq 8) = 1-P(X

P(X \geq 8) = 1-P(X

d. What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation?

The mean is 4 and the deviation is 2, so we want this probability

P(4\leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)

P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954

P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563

P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042

P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559

You might be interested in
Point Q is the centroid of △ABC. QE = _____
pychu [463]
That’s the answer to your question.

7 0
2 years ago
The length of the base of an isosceles triangle is x. The length of a leg is 4x-6. The perimeter of the triangle is 60. Find x.
lbvjy [14]

Answer:

Perimeter of a triangle = add all sides

Both the legs of the isosceles triangle are always EQUAL.

x+4x-6+4x-6 = 60

9x-12 = 60

9x = 60+12

9x = 72

x = 8

3 0
2 years ago
suppose Richard walks one kilometer every 10 minutes how many meters are there can you walk in an hour at this new rate
Ipatiy [6.2K]
One kilometer is 1000 meters.  One hour is 60 minutes, or six segments of 10 minutes each.  If you can walk 1000 meters in 10 minutes, you can walk 6000 in an hour (that is REALLY fast, by the way)
3 0
3 years ago
So if i can buy 4 basketballs for $44 at the same rate how much would 8 basket balls be?
ch4aika [34]
$88 for 8 basketballs bc 1 ball is 11$ and 11(8)=88
7 0
2 years ago
Read 2 more answers
What is b1 and r of geometrical sequence if b3 −b1 = 16 and b5 −b3 = 144.
Naily [24]

Answer:

b1 = 2 ; r = 3

Step-by-step explanation:

Given that :

if b3 −b1 = 16 and b5 −b3 = 144.

For a geometric series :

Ist term = a

Second term = ar

3rd term = ar^2

4th term = ar^3

5th term = ar^4 ;...

If b3 - b1 = 16;

ar^2 - a = 16

a(r^2 - 1) = 16 - - - (1)

b5 - b3 = 144

ar^4 - ar^2 = 144

ar^2(r^2 - 1) = 144 - - - - (2)

Divide (1) by (2)

a(r^2 - 1) / ar^2(r^2 - 1) = 16 /144

a / ar^2 = 1 / 9

ar^2 = 9a

Substitute for a in ar^2 - a = 16

9a - a = 16

8a = 16

a = 2

From ar^2 - a = 16

2r^2 - 2 = 16

2r^2 = 16 + 2

2r^2 = 18

r^2 = 18 / 2

r^2 = 9

r = √9

r = 3

Hence ;

a = b1 = 2 ; r = 3

7 0
3 years ago
Other questions:
  • Express the fractions 1/2, 3/16, and 7/8 with an LCD.
    8·1 answer
  • What is 0.0004 in its standard form ?
    14·2 answers
  • Four expressions are shown below:
    10·1 answer
  • 1. 39 = 1 3/10b<br><br> 2. 2/5g = 3/5
    13·2 answers
  • What is 89972 rounded by the 3rd significant number
    9·1 answer
  • Factor out the coefficient of the variable for 2.4n + 9.6 and -6z + 12
    13·1 answer
  • Drag each tile to the correct box.
    6·1 answer
  • Please help with number 8. And if you can explain how you got the answer please do and I’ll give brainliest
    15·1 answer
  • Can some please help with this
    8·2 answers
  • Find any stationary points of the graph of <img src="https://tex.z-dn.net/?f=y%20%3D%202x%5E2%20%2B%20e%5E-x%5E4" id="TexFormula
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!