A robot is deployed on Mars to study the presence of organic material. It is estimated that its lifespanT will follow the probabilistic lawP(T > t) = e-/3.This equation can be interpreted as saying that the probability that the robot will work at least Tyears is a decaying exponential. For instance, the probability that the robot will last one year ormore isP(T > 1) = e¬1/3 = 0.72The robot is deployed, and after three years it is still working. What is the probability that it willbreak at the end of the fourth year?

# Given : life span of a robot on planet Mars follow exponential distribution with probabilistic law…

Answered: A robot is deployed on Mars to study…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Exercise 9. Suppose that the lifespan (in years) of a water heater is modeled as Y - Expon(mean = 8). (a) Given that the unit is working at 3 years, compute the chances it will fail in the next year. (b) Given that the unit is working at 18 years, compute the chances it will fail in the next year. (c) Comment on the reasonableness of this Exponential model.
6. A home improvement store carries two models of power drills. Lifetime (i.e., time to failure) of Model 1 drills are exponentially distributed with a rate of of 0.15 failures per year, whereas Model 2 drills have a lifetime that is log-normally distributed with parameters u = 0.75 and o = 1.2. (a) Which model of power drill is more likely to fail within a year? (b) Which brand produces cables that are more likely to last at least 2 years? (c) Which model of power drill has longer expected lifetime?
The Striket Riche Company has begun drilling for oil. It anticipates 130 hour of drilling time before reaching the oil. Experience has shown that the drill bits it uses in this type of rock formation have a lifetime that is lognormal with tmed = 2 hr and s=0.91. The company currently has 35 drill bits available. What is the probability of striking oil before it runs out of bits?
Imagine that COVID-19 had spread exponentially in Maine since the first case (on March 12). Using the model f(t)=A02t/d with A0=1 and t= number of days since March 12, find D with the knowledge that there were 7,603 total cases on Nov. 7, 240 days after March 12.
4. You point your Geiger counter at a banana, waiting for it to click. You know that the time you have to wait is exponentially distributed with rate >= 1 Unfortunately, 10% of all Geiger counters have been sabotaged by Big Banana. A sabotaged Geiger counter, when pointed at a banana, will instead click after every 60 seconds to lull you into complacency. (a) Determine the CDF of the waiting time until your Geiger counter clicks (you do not know if your Geiger counter has been sabotaged). (b) If you have been waiting for 30 seconds and your Geiger counter still hasn't clicked yet, what is the probability that it has been sabotaged?
The Striket Riche Company has begun drilling for oil. It anticipates 130 hour of drilling time before reaching the oil. Experience has shown that the drill bits it uses in this type of rock formation have a lifetime that is lognormal with tmed = 2 hr and s=0.91. The company currently has 35 drill bits available. What is the probability of striking oil before it runs out of bits?

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