Let x be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. the article "methodology 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?

a)

b)

c)

d)

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

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

And f(x)=0 for other case.

For this distribution the expected value is the same parameter

 , ,

a. Compute both P(X≤4) and P(X<4).

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

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?

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

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

this doesn't make sense lol