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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suppose that the lifetime of a light bulb is exponentially distributed with mean 2 years. what is the expected value of this lifetime given that lifetime is between 1 to 3 years? e[x | 1 < x < 3] = ?
Suppose the probability π(x)π(x) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in metres) from the target is well-fitted by a logistic regression equation withlog(π(x)/[1−π(x)])=6.1−0.13xPlease answer below to 3 significant digits.Part a)For this prediction model, what is the probability of reaching the target from a distance of 49 metres.Part b)At what distance is the probability of reaching the target equal to 0.6?
The following table shows world population N, in billions, in the given year. According to the logistic model N = 10.90 / 1+2.23e^-0.030t, when will world population reach 90% of carrying capacity? Year N 1965 3.38 1970 3.72 1975 4.15 1980 4.48 1985 4.87 1990 5.38 1995 5.72 1999 6.05 a) 2064b) 2069c) 2066d) 2094
5.9-1: please help with part C:
IQuestion 3] A. Compute the value of x in the following i. 4* = 32 ii. 25B*+1) = 625 B. Express the following as a single logarithm i. % log 25 – 2log 3 +2log 6 ii. log (x+1)–log (x²-1) C. A culture of bacteria starts with 500 bacteria and increases exponentially. The relationship between the number of bacteria present B present in the culture and the time elapsed, d in days is modelled by the following equation B = 50 10 In how many days will the culture reach 1 600000 bacteria?
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?
In simple linear regression analysis, all the variables are in their natural logs to ensure that P37 Select one: a. None of the answers are correct b. $ log ⁡xy= log ⁡x+ log ⁡y $ c. $ log⁡ \frac{x}{y}= log⁡x- log⁡y $ d. $ log⁡ x^2 = n log⁡ x $
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.
A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.
Q1. 807 people were randomly selected and data was collected on whether or not they smoked cigarettes in the past 12 months (smoked = 1 if they did, smoked = 0 otherwise), their years of schooling (educ), the natural log of their annual income in dollars (In[income]), age in years (age), and race (white = 1 if white, white = 0 otherwise). The following logit models were estimated and the results are summarized in the table below. The numbers in parentheses are the standard errors. (1) logit (2) logit (3) sample average constant 1.43 0.02 (0.40) (1.06) educ -0.10 -0.11 12 (0.03) (0.03) In[income] 0.16 10.8 (0.11) age -0.02 -0.02 41 (0.0004) | (0.0004) white 0.02 0.7 (0.23) log-likelihood -525 -524 In column (2), the regression equation for smokeď* is: smoked* = x'3 + e = B1 + B2educ + B3 In[income] + B4age + B5white + e In column (3), the sample averages of the regressors are listed. For example, 12 is the sample average of educ, 10.8 is the average of In[income], etc. (a) Using the…

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