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5. (10 points) let T-Weibull(a,B 3) be the lifetime of an electronic part. If n parts are put on ...
At time t 0, 21 identical components are tested. The lifetime distribution of each is exponential...
At time t 0, 21 identical components are tested. The lifetime distribution of each is exponential with parameter A. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y 12 of the 21 components are still in operation (so 9 have failed). Derive the mle of A. [Hint: Let Y the number that survive 24 hours. Then Y Bin(n, p). What is the mle of p?...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
3. (10 points) The life of an electronic equipment is a r.v. X whose p.d.f is f(z;θ)-Be 4xz > 0,0...
3. (10 points) The life of an electronic equipment is a r.v. X whose p.d.f is f(z;θ)-Be 4xz > 0,0>0, and let be its expected lifetime. On the basis of the random sample Xi,..X from this distribution, derive the MP test for testing the hypothesis Ho:to against the alternative HA:-(>o) at level of significance o
3. (10 points) The life of an electronic equipment is a r.v. X whose p.d.f is f(z;θ)-Be 4xz > 0,0>0, and let be its expected...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
5. 20 points) Let n 3 be an integer. Let S, be the permutation group on...
5. 20 points) Let n 3 be an integer. Let S, be the permutation group on n letters. a) (10 points) Find explicitly , TE S, such that T *o-To. Prove your answer. c) (10 points) Find explicitly an injective map f: (Z3, +a) →S, which satisfies the homomorphism property. Prove your answer.
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the nu...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
7. (10 pts) Derive an approximation to the risk-neutral price of an American put option having parameters S-10, T= 0.25, K = 10, σ and q 0. Use 3 time periods (n 3). -0.2, r-0.05, 7. (10 pts...
7. (10 pts) Derive an approximation to the risk-neutral price of an American put option having parameters S-10, T= 0.25, K = 10, σ and q 0. Use 3 time periods (n 3). -0.2, r-0.05,
7. (10 pts) Derive an approximation to the risk-neutral price of an American put option having parameters S-10, T= 0.25, K = 10, σ and q 0. Use 3 time periods (n 3). -0.2, r-0.05,
5. Let f a, b R be a 4 times continuously differentiable function. For n even, consider < tn = b, a to < t< an...
5. Let f a, b R be a 4 times continuously differentiable function. For n even, consider < tn = b, a to < t< an uniform partition of [a, b] with b- a , i = 0,1,.. , n - 1 h t Let T denote the composite Trapezoidal rule associated with the above partition which approx imates eliminate the term containing h2 in the asymptotic expansion. Interprete the result which you obtain as an appropriate numerical quadrature rule...
part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulativ...
part a, b and c please
Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulative distribution fpaction of (e) What is the probability that, of 3 of these lampe, at keast 2 will function for at least 15 hours? Assume that the 3 lamps function/fail independent of each other 7
Problem 4. (15 points) The...
5-4 Solve the problem. Keep 3 decimal places. 10. 10. Use the formula f (t) yob'. In 2007 China exported $2 billion worth of vehicle parts. By 2014, these exports reached $12 billion. Let t-0...
5-4 Solve the problem. Keep 3 decimal places. 10. 10. Use the formula f (t) yob'. In 2007 China exported $2 billion worth of vehicle parts. By 2014, these exports reached $12 billion. Let t-0 correspond to 2007. Find the value of exports in 2020.
5-4 Solve the problem. Keep 3 decimal places. 10. 10. Use the formula f (t) yob'. In 2007 China exported $2 billion worth of vehicle parts. By 2014, these exports reached $12 billion. Let t-0...
At time t 0, 21 identical components are tested. The lifetime distribution of each is exponential with parameter A. The experimenter then leaves the test facility unmonitored. On his return 24 hours later, the experimenter immediately terminates the test after noticing that y 12 of the 21 components are still in operation (so 9 have failed). Derive the mle of A. [Hint: Let Y the number that survive 24 hours. Then Y Bin(n, p). What is the mle of p?...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
3. (10 points) The life of an electronic equipment is a r.v. X whose p.d.f is f(z;θ)-Be 4xz > 0,0>0, and let be its expected lifetime. On the basis of the random sample Xi,..X from this distribution, derive the MP test for testing the hypothesis Ho:to against the alternative HA:-(>o) at level of significance o
3. (10 points) The life of an electronic equipment is a r.v. X whose p.d.f is f(z;θ)-Be 4xz > 0,0>0, and let be its expected...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
5. 20 points) Let n 3 be an integer. Let S, be the permutation group on n letters. a) (10 points) Find explicitly , TE S, such that T *o-To. Prove your answer. c) (10 points) Find explicitly an injective map f: (Z3, +a) →S, which satisfies the homomorphism property. Prove your answer.
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
7. (10 pts) Derive an approximation to the risk-neutral price of an American put option having parameters S-10, T= 0.25, K = 10, σ and q 0. Use 3 time periods (n 3). -0.2, r-0.05,
7. (10 pts) Derive an approximation to the risk-neutral price of an American put option having parameters S-10, T= 0.25, K = 10, σ and q 0. Use 3 time periods (n 3). -0.2, r-0.05,
5. Let f a, b R be a 4 times continuously differentiable function. For n even, consider < tn = b, a to < t< an uniform partition of [a, b] with b- a , i = 0,1,.. , n - 1 h t Let T denote the composite Trapezoidal rule associated with the above partition which approx imates eliminate the term containing h2 in the asymptotic expansion. Interprete the result which you obtain as an appropriate numerical quadrature rule...
part a, b and c please
Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulative distribution fpaction of (e) What is the probability that, of 3 of these lampe, at keast 2 will function for at least 15 hours? Assume that the 3 lamps function/fail independent of each other 7
Problem 4. (15 points) The...
5-4 Solve the problem. Keep 3 decimal places. 10. 10. Use the formula f (t) yob'. In 2007 China exported $2 billion worth of vehicle parts. By 2014, these exports reached $12 billion. Let t-0 correspond to 2007. Find the value of exports in 2020.
5-4 Solve the problem. Keep 3 decimal places. 10. 10. Use the formula f (t) yob'. In 2007 China exported $2 billion worth of vehicle parts. By 2014, these exports reached $12 billion. Let t-0...
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