Assume the distributions of the Strength H and Stress S are all Normal distribution or Exponential distribution, such as 1) HN(100,10²), S~N(50,10²) 2) fg (h)=0.005e-0.005/ 0≤h<∞ f (s) = 0.05e-0.05s 0≤s<∞0 Derive reliability calculation formula by stress-strength model (the derivation process is required), and give the calculated value of reliability.|

Assume the distributions of the Strength H and Stress S are all Normal distribution or Exponential distribution, such as 1) HN(100,10²), S~N(50,10²) 2) fg (h)=0.005e-0.005/ 0≤h<∞ f (s) = 0.05e-0.05s 0≤s<∞0 Derive reliability calculation formula by stress-strength model (the derivation process is required), and give the calculated value of reliability.|

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

See similar textbooks

Similar questions

Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
(3) Let X = b >(8,-) find E(5+6x) and distribution function.
The failure time (T) of an electronic circuit board follows exponentially distribution with failure rate λ = 10−4/h. What is the probability that (i) it will fail before 1000 h? (ii) it will survive at least 10,000 h ? (iii) it will fail between 1000 and 10,000 h? (iv)Determine the mean time to failure. .
Based on an analysis of sample data, an article proposed the pdf f(x) = 0.55e-550x-1) when x 21 as a model for the distribution of X= time (sec) spent at the median line. (Round your answers to three decimal places.) (a) What is the probability that waiting time is at most 4 sec? More than 4 sec? at most 4 sec P(X 4) = more than 4 sec P(X> 4) = (b) What is the probability that waiting time is between 6 and 9 sec?
Q6. Let us assume that the lifetime of light bulbs follows an exponential distribution with the pdf: f(x) = A exp(-Ax) We test 10 bulbs and their lifetimes are 5, 3, 5, 1, 7, 3, 4, 8, 2, 3 years, respectively. What is the MLE for A? What is the method of moments estimator for A?
The time (in hours) required to repair a machine is exponentially distributed 1 with parameter 2 = = what is the probability that the repair time exceeds 3 3
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. Find the probability that the patient would die before receiving transplant.
Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf f(x, y) ĮK(x? + y?) 21 25). (Round your answer to three decimal places.) P(Y > 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psi
Suppose that an item has a hazard rate function X(t) = 2.4t², t> 0. What is the probability that (a) the item survives to age 0.5? (b) the item's lifetime is between 1.5 and 3? (c) a (-year-old item will survive to age 3?
The normal distribution is a bell-shaped curve defined by f(x) = e-x' , x € [-4,4] Optimize the function when xo = 1 and stop the calculation when A x = 0.1