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1. An insurer is combining two independent blocks of insurance....
12 marks Let independent random samples of sizes n and n2 be taken respectively from two normal distributions with unkn...
12 marks Let independent random samples of sizes n and n2 be taken respectively from two normal distributions with unknown means 1 and 2 and unknown variances oand o. Denote the two samples by . . ,Jn, and y,... , yn2: Which have means T and T, and sample variances s and s2, respectively (a) 4 marks Show that when of = o2, the likelihood ratio test statistic for testing Ho 12 against H 2 can be written as T2...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
1. Derive the exact distribution to test the independence for the 2 x 2 contingency table Respons...
1. Derive the exact distribution to test the independence for the 2 x 2 contingency table Response 1 n1 n12 n1+ 2 n21 n22 n2+ +1 m+2 The hypergeometric distribution can be used to find the probability of observing a particular 2x2 table under independence . In the independent binomial model, we observe two random variables, Nu and N21 . We use the observed values n1u and n21 to compare the respective probabilities of success, π1 and π2 . The...
The Binomial and Poisson Distributions Both the Binomial and Poisson Distributions deal with discrete data where...
The Binomial and Poisson Distributions Both the Binomial and Poisson Distributions deal with discrete data where we are counting the number of occurrences of an event. However, they are very different distributions. This problem will help you be able to recognize a random variable that belongs to the Binomial Distribution, the Poisson Distribution or neither. Characteristics of a Binomial Distribution Characteristics of a Poisson Distribution The Binomial random variable is the count of the number of success in n trials: number of...
4. Comparing two population proportions (independent samples)
4. Comparing two population proportions (independent samples) Most major survey research organizations do not include wireless telephone numbers when conducting random-digit-dial telephone surveys. If there are differences between persons with and without landline phones, using a random-digit-dial telephone survey may introduce bias into the survey results. Data on a broad range of health topics are collected through personal household interviews of a representative sample of the U.S. civilian noninstitutionalized population in the National Health Interview Survey (NHIS) respondents are also asked about...
Could you please answer the question Q1 to Q3. Write the answer clearly and step by step. 1 Let U = {1, 2, 3, 4, 5, 6, 7} be the universe. Form the set A as follows: Read off your seven digit student...
Could you please answer the question Q1 to Q3. Write the answer
clearly and step by step.
1 Let U = {1, 2, 3, 4, 5, 6, 7} be the universe. Form the set A as follows: Read off your seven digit student number from left to right. For the first digit ni include the number 1 in A if ni is even otherwise omit 1 from A. Now take the second digit n2 and include the number 2 in...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is a picture of a bolt. The D indicates Below right is a side and overhead picture of a nut. The the diameter of the bolt D indicates the diameter of the hole INSIDE the nut. ATI RODI c ISO METRIC AND WASHERS A bolt is supposed to fit inside a nut. On the right is a picture of a bolt properly fitting inside a...
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE o...
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE of λ based on (Yi,Yo) (b) Show that the estimator λ (Y + Y)/3 is unbiased for λ and compute its variance. (c) With as much rigor as possible, show that if A is large then (A-X)/v is approximately normally distributed. (d) Derive a 95 percent confidence interval for A based on the asymptotic distribution of λ in part (c) (e) Extra Credit Based on part...
hi i need answer from part d Question 2 (48 marks) Consider a firm which produces a good, y, using two factors of...
hi i need answer from part d
Question 2 (48 marks) Consider a firm which produces a good, y, using two factors of production, xi and x2 The firm's production function is Note that (4) is a special case of the production function in Question 1, in which α-1/2 and β-14. Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously...
Q1) Consider two events P and Q. a. Write the general formula used to calculate the probability that either event P occu...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
12 marks Let independent random samples of sizes n and n2 be taken respectively from two normal distributions with unknown means 1 and 2 and unknown variances oand o. Denote the two samples by . . ,Jn, and y,... , yn2: Which have means T and T, and sample variances s and s2, respectively (a) 4 marks Show that when of = o2, the likelihood ratio test statistic for testing Ho 12 against H 2 can be written as T2...
3. (a) The bus 500 arrives at Liverpool Airport at a rate of A buses per hour. Assume that the arrivals form a Poisson process. Let X (t) be the number of buses that arrive in t hours. X(t) is distributed as Px(o(u)=e-Ar (Xt)" u! when u is a positive integer and 0 otherwise. Let Y be the amount of time that you must wait for the 3rd bus to arrive. The event X (t) < 3 (fewer than three...
1. Derive the exact distribution to test the independence for the 2 x 2 contingency table Response 1 n1 n12 n1+ 2 n21 n22 n2+ +1 m+2 The hypergeometric distribution can be used to find the probability of observing a particular 2x2 table under independence . In the independent binomial model, we observe two random variables, Nu and N21 . We use the observed values n1u and n21 to compare the respective probabilities of success, π1 and π2 . The...
Could you please answer the question Q1 to Q3. Write the answer
clearly and step by step.
1 Let U = {1, 2, 3, 4, 5, 6, 7} be the universe. Form the set A as follows: Read off your seven digit student number from left to right. For the first digit ni include the number 1 in A if ni is even otherwise omit 1 from A. Now take the second digit n2 and include the number 2 in...
8. You are given two boxes, one contains nuts and the other contains bolts. Below is a picture of a bolt. The D indicates Below right is a side and overhead picture of a nut. The the diameter of the bolt D indicates the diameter of the hole INSIDE the nut. ATI RODI c ISO METRIC AND WASHERS A bolt is supposed to fit inside a nut. On the right is a picture of a bolt properly fitting inside a...
1. Suppose YPoisson(A) and Y2 ~Poisson(2X) are two independent observations. (a) Derive the MLE of λ based on (Yi,Yo) (b) Show that the estimator λ (Y + Y)/3 is unbiased for λ and compute its variance. (c) With as much rigor as possible, show that if A is large then (A-X)/v is approximately normally distributed. (d) Derive a 95 percent confidence interval for A based on the asymptotic distribution of λ in part (c) (e) Extra Credit Based on part...
hi i need answer from part d
Question 2 (48 marks) Consider a firm which produces a good, y, using two factors of production, xi and x2 The firm's production function is Note that (4) is a special case of the production function in Question 1, in which α-1/2 and β-14. Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
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