Surge protection of a piece of sensitive medical equipment is analyzed. Surge in

Question

Surge protection of a piece of sensitive medical equipment is analyzed. Surge intensity is classified as "low"(voltage increases by less than 5% of the nominal value), "medium" (5%- 15%0, "high" (15%-40%), and "detrimental" (voltage increase exceeds 40% of the nominal value). For a particular site, the probability that no surge occurs during a two-hour operation is estimated to be 0.75. It is also known that, on average, high-intensity surges occur 5 times more often than detrimental once, medium-intensity surges occur three times more often than high-intensity ones, and low-intensity surges happen twice as often as medium-intensity ones. Assume that no more than one surge will occur during the operation. What is the probability mass function of a random variable X, where x = 0 means that no surge has occurred, X = 1 means that a low-intensity surge has occurred, X = 2 that a medium-intensity one has occurred, and X = 3 means that a high-intensity surge was detected, and finally X= 4 stands for a detrimental surge? What is the probability that neither high-intensity nor detrimental surge occur during the operation?

Explanation / Answer

so we have the sample space consisting of {0,1,2,3,4} and it is given that P{X=0} (no surge)=0.75 0=no surge 1=low 2=medium 3=high 4=detrimental it is given in the problem that: P(3)=5*P(4) P(2)=3*P(3) P(1)=2*P(2) P(0)=0.75 P(0) + P(1) + P(2) + P(3) + P(4)=1 P(1) + P(2) + P(3) + P(4)=0.25 2*P(2) + P(2) + P(3) + P(4)=0.25 2*3*P(3) + 3*P(3) + P(3) + P(4)=0.25 2*3*5*P(4) + 3*5*P(4) + 5*P(4) + P(4)=0.25 30P(4) + 15P(4) + 5P(4) + P(4)=0.25 56*P(4)=0.25 P(4)=1/(224) P(3)=5*P(4) [GIVEN] P(3)=5*1/224 P(3)=5/224 P(2)=3*P(3) [GIVEN] P(2)=3*5/224 P(2)=15/224 P(1)=2*P(2) [GIVEN] P(1)=2*15/224 P(1)=30/224 P(0)=0.75 [GIVEN] P(0)=3/4 P(0)=168/224 pmf= : P(0)=168/224 P(1)=30/224 P(2)=15/224 P(3)=5/224 P(4)=1/(224) b.) P(neither 3 nor 4 occur)=1-P(3)-P(4)=224/224 - 5/224 - 1/224 = 218/224

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.