Q.9) Given that, X ~ Poisson (μ = 4)
E(X) = 4 and Var(X) = 4 and SD(X) =
a) We want to find, P(X ≤ 4)
Using Excel we find this probability,
P(X ≤ 4) = POISSON (4, 4, 1) = 0.628837
Therefore, required probability is 0.628837
b) Expected number of material anomalies occuring in that region is 4
c) mean + sd = 4 + 2 = 6
We want to find, P(X > 6)
P(X > 6)
= 1 - P(X ≤ 6)
= 1 - POISSON (6, 4, 1)
= 0.110674
Therefore, required probability is 0.110674
9. Let X be the number of material anomalies occurring in a particular region of an...
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"� proposes a Poisson distribution for X. Suppose that ? = 4. (Round your answers to three decimal places.) (a) Compute both P(X ? 4) and P(X < 4). (b) Compute P(4 ? X ? 5). (c) Compute P(5 ? X). (d) What is the probability that the number of anomalies does not...
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"t proposes a Poisson distribution for X. Suppose that μ-4. (Round your answers to three decimal places.) (a) Compute both P(X S 4) and P(X < 4). P(X < 4)- (b) Compute P(4 sX 9) (c) Compute P(9 sX) (d) What is the probability that the number of anomalies does not exceed the...
Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. A researcher proposes a Poisson distribution for X. Suppose that ? = 6 The Poisson probability mass function is: P(x-fr 0,1,2.. Use the pmf to calculate probabilities. Verify these values in R using dpois(x,lambda) Compute the following probabilities: (Round your answers to three decimal places.) (a) P(X-3)- (c) P(X< 3) (d) PX 3)-
Will rate!! Let X be the number of material anomalies occurring in a particular region of an aircraft gas turbine disk. A researcher proposes a Poisson distribution for x. Suppose that à 5 The Poisson probability mass function is: cA. Use the pmf to calculate probabilities. Verify these values in R using dpoistx,Jlambda). Compute the following probabilities: (Round your answers to three decimal places) (a) P(X 4) (c) Px 4) -
Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. A researcher proposes a Poisson distribution for X. Suppose that i = 6. The Poisson probability mass function is: 1 - 1 P(X = r) = r! for x = 0,1,2,... Use the pmf to calculate probabilities. Verify these values in R using dpois(x,lambda). Compute the following probabilities: (Round your answers to three decimal places.) (a) P(X = 5) = (b) PCX...
Let X denote the number of tornadoes occurring in a specific region in 2016. Assume X has a Poisson distribution with variance 7 (a) Calculate P(X26) (b) Caleulate the probability that there will be 8 or more tornadoes given that there are at least 3 tornadoes, e. P(X8X23)
SUppose that the number of failures in cast-iron pipe of a particular length has a Poisson distribution with mean μ=2.5. What is the probability that X exceeds it's mean?
The number if traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 6.4 a) Find the probability that less than 3 accidents will occur next month on this stretch of road. b) Find the mean and standard deviation of the number of traffic accidents.
Use Poisson Distribution to solve problems 6-7 6. Suppose that the average number of accidents occurring weekly on a particular stretch of a highway equals 2. What is the probability that within next week: a) 0 accidents occur P(x 0) (3 points) A) 0.1258 B) 0.1353 C) 0.8647 D) 0.2706 b) 1 or less accidents occur P( (5 points) 2)-
Let X be the number of “F1 tornados” that will hit the Twin Cities metro region next year (these are the least damaging tornados). Suppose X has a Poisson distribution with mean µ = 4.7. Find P(X = 3). Show your work with the formula involving the number e ≈ 2.7182818.