The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3.
Compute the following. (Round your answers to three decimal places.)
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3.
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3. Compute the following.
Suppose that the lifetime of a component (in hours), X, is modeled with a Weibull distribution with B 0.5 and = 3400. Determine the following in parts (a) and (b) Round your answers to three decimal places (e.g. 98.765) a) P(X> 3500) = i b) P(X> 6000|X > 3000) i c) Suppose that X has an exponential distribution with mean equal to 3400. Determine the following probability Round your answer to three decimal places (e.g. 98.765) P(X 6000X > 3000)...
The lifetime of a drill bit in a mechanical operation, in hours, has a Weibull distribution with α = 0.5 and β = 2.2. Calculate the probability that the bit will fail after 2.8 hours Answer using 4 decimals.
Suppose that the lifetime of a component (in hours), X is modelled with a Weibull distribution with a = 0.6. and λ = 1/4000. Determine the value for P(X > 5,961 | X > 3500) i.e Probability of X > 5,961 given tha X is greater than 3500. Please enter the answer to 3 decimal places.
Suppose that X has a Weibull distribution with B = 0.5 and 8 = 100 hours. Determine the following. Round the answers to 3 decimal places. (a) P(X < 10000) = (b) P(X > 5000) =
3. Suppose that X has the gamma distribution with parameters α and β. (a) Determine the mode of X. (Be careful about the range of a) (b) Let c be a positive constant. Show that cX has the gamma distribution with parar neters and ß/c.
Suppose that X has a gamma distribution with parameters α > 0 and β>0. Show that if a is any value so that α+a>0 then E[X^a] = (β^aΓ(α + a))/Γ(a)
5. For the Weibull distribution with parameters a and X, recall that for t> 0 the density function and distribution function are, respectively, f(t) = 410-1-(At) F(t) = 1 -e-(1)" Suppose that T has the Weibull distribution with parameters a = 1/2 and X = 9. (a) (4 points) Compute exactly P(1 <1 < 1.017 > 1). Show your work. Write your answer to 6 decimal places. (b) (4 points) Compute an approximation of P(1 <T < 1.01 T >...
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by That is, Y has a gamma distribution with parameters α = 2 and θ. Let denote the MLE of θ. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of θ. b Find E() and V(). c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What...
Suppose that the random variable X has a Weibull distribution with parameters a = 2.98 and λ = 0.23. Find P(3 ≤ X ≤ 7). Round your answer to the nearest ten thousandth.