. Find the probability that the lifetime of a given device exceeds 2 hours. 3. Find the probability that the lifetime of a given device exceeds 10 hours given that the life time already exceeded 9 hours. C. Find the probability that out of 3 devices, the lifetimes of at least 2 devices exceed 2 hours.
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- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
- Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the lifetime of a bulb is f(t)=14e−t/4,t≥0.What is the probability that the bulb will fail within 5 hours?John bought a second-hand car that was driven 16 kilometers (km) from sahibindenmiacaba.com. What is the probability that he will be able to drive this car at least for another 20 km before it has to be salvaged if life of a car (in km) is exponentially distributed with a rate parameter of 1/30? Answer uniformly distributed over (0, 140)? Answer
- Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2Personnel at an Engineering company use an online terminal to make routine engineering calculations. If the time each engineer spends in a session at a terminal has an exponential density function with expected value of 36 minutes, calculate the following. 1. What is the probability that each and everyone of five engineers spend less than 25 minutes at a terminal making routine calculations?2. Why would we use the same model we used? Does it make sense? Explain.In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function f(t) = 8 t 2 , t ≥ 8 where 8 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 28 and 56 seconds. (b) Find the probability that an animal chosen at random takes more than 28 seconds given that it took less than 56 seconds.
- A random sample of math majors taking an introductory statistics course were surveyed after completing the final exam. They were asked how many times they reviewed their final exam before handing it in to the professor? Results displayed in a probability density function for the randon variable x, the number of times students reviewed their exam before handing it in. Find the standard deviation of x. x P(X=x) 1 1/5 2 2/5 7 2/5Which of the following graphs you would recommend log transformation X' =ln[X] to best transform data into a normal distribution?If X ~ U(3, 15), what is the probability density function for this distribution?