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- b) Explain how X can be related to the exponential distribution by using a moment generating function argument.The digestion time (in hours) of a fixed amount of food is exponentially distributed with a = 1. a. Find the mean digestion time. b. Find the probability that the digestion time is less than 30 minutes.The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .
- solveIn random sampling from the exponential distribution, f(x) =1 θθe x− , x > 0, θ> 0, find the maximum likelihood estimator of θ and obtain the asymptotic distribution of this estimatorThe lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours. a) What is the probability that an assembly on test fails in less than 100 hours? b) Determine the interval of time that needs to pass for the mechanical assembly to fail is 0.1.suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
- Complete this PDF and find the expected value of X:What is the probability that x is less than or equal to 2? What is the probability that is an even number? Determine the cumulative destribution function for the function F(3)For binomial distribution, E(X) is the expectation. How to induce E(X^2) in terms of E(X). Thanks
- The random variable X is exponentially distributed, where X represents the waiting time to see a shooting star during a meteor shower. If X has an average value of 45 seconds, what are the parameters of the exponential distribution?The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of10 minutes.a) Suppose that you have already been waiting for one hour for a taxi. What is the probability thatone arrives within the next 10 minutes?b) Determine x such that the probability that you wait more than 10 minutes is 0.10?c) Find the probability distribution of the number of taxis for 10 minutes.Let X|Λ have an exponential distribution with conditional survival function SX|Λ(x|λ) = e−λx. Let Λ have a Gamma distribution with parameters α and θ. Find the unconditional or marginal survival function of X.