The survival function is S(t) = 1 − F(t), or the probability that a person/machine/business lasts...

The survival function is S(t) = 1 − F(t), or the probability that a person/machine/business lasts longer than t time units. The hazard function is h(t) = f(t)/S(t). Here F(t) is the cdf and f(t) is the pdf. It is the probability that the person/machine/business dies in the next instant, given that it survived to time t. Determine the hazard function for the Exponential(λ) distribution. How does the expression for the exponential hazard function related to the memoryless property of the exponential distribution (explain in words)?

Expert Solution

orchestra answered 2 years ago

Find the Laplace transforms: F(s)=L{f(t)} of the function f(t)=(8−t)(u(t−2)−u(t−5)), for s≠0. F(s)=L{f(t)}=

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t <...

f(t) = 1- t 0<t<1 a function f(t) defined on an interval 0 < t < L is given. Find the Fourier cosine and sine series of f and sketch the graphs of the two extensions of f to which these two series converge

1. Which of the following is(are) required condition(s) for a discrete probability function? ∑f(x) = 0...

1. Which of the following is(are) required condition(s) for a discrete probability function? ∑f(x) = 0 f(x) ≥ 1 for all values of x f(x) < 0 None of the answers is correct. 2.Let Z be the standard normal random variable. What is P(0<Z<2.50)? 0.4640 0.4938 0.3519 0.4028 None of the above 3. A researcher has collected the following sample data. 5 12 7 9 5 6 7 5 13 4 The 90th percentile from Excel Functional work is 12...

6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for −...

6. The function f(t) = 0 for − 2 ≤ t < −1 −1 for − 1 ≤ t < 0 0 for t = 0 1 for 0 ≤ t < 1 0 for 1 ≤ t ≤ 2 can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function...

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function of time t. Graph f together with the velocity function ?v(t)equals=StartFraction ds Over dt EndFractiondsdtequals=f prime left parenthesis t right parenthesisf?(t) and the acceleration function ?a(t)equals=StartFraction d squared s Over dt squared EndFractiond2sdt2equals=f prime prime left parenthesis t right parenthesisf??(t)?, then complete parts? (a) through? (f). sequals=112112tminus?16 t squared16t2?, 0less than or equals?tless than or equals?77 ?(a heavy object fired straight up from? Earth's...

The probability of winning on a lot machine is 5%. If a person plays the machine...

The probability of winning on a lot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. A travel survey of 1500 Americans reported an average of 7.5 nights stayed when they went on vacation. Find a point estimate of the population mean. If we can assume the population standard deviation is 0.8 night, find the 95% confidence interval for the true mean. SHOW...

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)=...

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)= 3) Find the Laplace transform of f(t)=u(t−6)⋅t^2 F(s)=

1. Let g(s) = √ s. Find a simple function f so that f(g(s)) = 0....

1. Let g(s) = √ s. Find a simple function f so that f(g(s)) = 0. Hint: see Methods of computing square roots on Wikipedia. Use Newton’s method to estimate √ 2. Start with 3 different (and interesting) initial values of your choice and report the number of iterations it takes to obtain an accuracy of at least 4 digits. In python.

T/F 1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear...

T/F 1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear function, where x = (x1,...,xn). 2) The function f(x1,x2,x3,x4) = (x2,x1,x4,x3) is linear. 3) For a given matrix A and vector b, equation Ax = b always has a solution if A is wide

proof: L t^(n+1)f(t)=(-1)^(n+1)(d^(n+1)/ds^(n+1))*F(s)

proof: L t^(n+1)*f(t)=(-1)^(n+1)*(d^(n+1)/ds^(n+1))*F(s)

Question