A lifetime test is carried out on a particular type of componentA total of 10 components are observed, with failure times as follows:0.3, 7.7, 6.3, 4.2, 1.6, 5.6, 6.3, 8, 5.1, 1.7.The failure times are assumed to be iid Exponential with hazard rate λ.Determine the maximum likelihood estimate  of λ.(Give answers to 3 decimal places)

Question 3. [9 Marks]. Recall that the exponential PDF has the form f (t; λ) = λe−λtwhere t, λ > 0 and λ is known as the rate parameter. Consider a job shop that consists of3 identical machines and 2 technicians. Suppose that, the amount of time each machineoperates before breaking down is exponentially distributed with rate parameter 0.1, and theamount of time a technician takes to fix a machine is exponentially distributed with rateparameter 0.4. Suppose that all the times to breakdown and times to repair are independentrandom variables and let X(t) be the number of machines which are operating at time t.(a) Determine the Q-matrix for this Markov process.(b) Write the forward equations involving the P ′0j (t), j = 0, 1, 2, 3, in terms ofpj (t) := P0j (t) = P(X(t) = j|X(0) = 0).(c) Obtain the equilibrium probabilities pj = limt→∞ pj (t).(d) What is the average number of busy technicians in the long-run? [Note: do not expectyour answer to be an integer.]

We observe 11 components, starting from time t = 0. The component life times are independent. Observation ends immediately following the 9th failure, which occurs at time t = 13.48. Give (correct to 2 decimal places) an appropriate estimate for F(13.48), using the Mean ranking metho

The commulative distribution of a component is given as F(t) = 0.2e^(-0vt) of the range of the random variable T= 3 ≤ t ≤ αbr Determine the mean time to failure MTTF What is the probability that the component will fail 10hrs

Which distribution does the decay parameter belong to?Question 2Answera.Uniform Distributionb.Poisson distributionc.Exponential di

Suppose a manufacturer wants to estimate the averagelifespan of a new product they have developed. Theyrandomly select 15 products and test them until they fail.It is known that the average lifespan is 120 hours, with astandard deviation of 10 hours. Assume that the lifespanof the products follows a normal distribution. Themanufacturer wants to know the probability that theaverage lifespan of the product is greater than 130 hours.