1. Let sample space S={1, 2, 3, 4, 5, 6}. Is it this a true or...
1. Let sample space S={1, 2, 3, 4, 5, 6}. Is it this a true or false statement : event C{1,2,3} and D={4,5,6} are both mutually exclusive and collectively exhaustive? My teacher said this is True please explain why in a picture and explanation
2.Let sample space S={1, 2, 3, 4, 5, 6}. Is it this a true or false statement : event E={3,4,5} and F={1,2,3} do not form a partition? My teacher said this is True please explain why in a picture and explanation
Homework Answers
Problem 1.2 Consider an experiment with sample space S = {1,2,3,4}. Define events A, B, C...
Problem 1.2 Consider an experiment with sample space S = {1,2,3,4}. Define events A, B, C as A = {1,2}, B = {2,3}, C = {1,4}. (a) Are A, B, C mutually disjoint? Are A, B, C collectively exhaustive? (b) Is it possible to have P[A] + P[B] + P[C] = 1? Explain why or why not. (c) If P[A] + P[B] + PIC] = 1, what is the value of P[A]?
Let a sample space be partitioned into three mutually exclusive and exhaustive events, py, 2, and,Ie....
Let a sample space be partitioned into three mutually exclusive and exhaustive events, py, 2, and,Ie. Complete the following probability table. (Round your answers to 2 decimal places.) Conditional Probabilities Prior Joint P(Bi) 0.11 PIA B)0.46 P(An B) P(B I A) P(83 1 A) Total P(A)
#5 (4 pts.) Consider the following sample space S and events A and B. s-(-4 <...
#5 (4 pts.) Consider the following sample space S and events A and B. s-(-4 < x < 2, 6 < x < 12), A={-4 < x < 0}, B=(-1 x<2), A and B are: a. (mutually exclusive, independent) b. (mutually exclusive, dependent) c. (non-mutually exclusive, independent) d. (non-mutually exclusive, dependent) #6 (4 pts.) In problem #5 P(B-A)- c. 1/4 d. 1/6
1.Let Ai, A2,. . , Ak be collection of sets that partitions the sample space S....
1.Let Ai, A2,. . , Ak be collection of sets that partitions the sample space S. Which of the following are properties of the partition? B. Ain A2nnAk S. C. The sets A, A are mutually exclusive D. The sets A1, A2,... Ak are independent. E. Only A. and B. F. Only A. and C. G. Only A. and D. H. Only B. and C. I. Only B. and D. J. Only C. and D. K. Only A., B., and...
True or False With explanation please. 1- True or false: a. If A is an event...
True or False With explanation please.
1- True or false: a. If A is an event of a sample space with P(A)-P(AS), then P(A)-0.5 b. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one P(A or B)-P(A)+P(B) P(A and B) P(A).P(B) by its own probability and then adding all the products together; that is P deviation of σ. If x is converted to the...
Discuss the validity of the following statement. If the statement is always true, explain why. If...
Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. IfE and F are complementary events, then E and F are mutually exclusive. Choose the correct answer below. O A. The statement is true because if E and F are complementary events, then EnF is equal to the sample space. B. The statement is false because the null set is an element of both E and F. Therefore, E and...
Discuss the validity of the following statement. If the statement is always true, explain why. If...
Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are complementary events, then E and F are mutually exclusive. Choose the correct answer below. A. The statement is true because two complementary events have to be mutually exclusive. B. The statement is true because if E and F are complementary events, then EnF is equal to the sample space. C. The statement is false because...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB)...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and,...
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3. Complete the following probability table. (Round your answers to 2 decimal places.) Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities P(B1) = 0.11 P(A | B1) = 0.45 P(A ∩ B1) = P(B1 | A) = P(B2) = P(A | B2) = 0.62 P(A ∩ B2) = P(B2 |A) = P(B3) = 0.38 P(A | B3) = 0.85 P(A ∩ B3) = P(B3...
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and,...
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and, B3. Complete the following probability table. (Round your answers to 2 decimal places.) Prior Probabilities Conditional Probabilities Joint Probabilities Posterior Probabilities P(B1) = 0.15 P(A | B1) = 0.40 P(A ∩ B1) = P(B1 | A) = P(B2) = P(A | B2) = 0.65 P(A ∩ B2) = P(B2 |A) = P(B3) = 0.32 P(A | B3) = 0.75 P(A ∩ B3) = P(B3...
Problem 1.2 Consider an experiment with sample space S = {1,2,3,4}. Define events A, B, C as A = {1,2}, B = {2,3}, C = {1,4}. (a) Are A, B, C mutually disjoint? Are A, B, C collectively exhaustive? (b) Is it possible to have P[A] + P[B] + P[C] = 1? Explain why or why not. (c) If P[A] + P[B] + PIC] = 1, what is the value of P[A]?
Let a sample space be partitioned into three mutually exclusive and exhaustive events, py, 2, and,Ie. Complete the following probability table. (Round your answers to 2 decimal places.) Conditional Probabilities Prior Joint P(Bi) 0.11 PIA B)0.46 P(An B) P(B I A) P(83 1 A) Total P(A)
#5 (4 pts.) Consider the following sample space S and events A and B. s-(-4 < x < 2, 6 < x < 12), A={-4 < x < 0}, B=(-1 x<2), A and B are: a. (mutually exclusive, independent) b. (mutually exclusive, dependent) c. (non-mutually exclusive, independent) d. (non-mutually exclusive, dependent) #6 (4 pts.) In problem #5 P(B-A)- c. 1/4 d. 1/6
1.Let Ai, A2,. . , Ak be collection of sets that partitions the sample space S. Which of the following are properties of the partition? B. Ain A2nnAk S. C. The sets A, A are mutually exclusive D. The sets A1, A2,... Ak are independent. E. Only A. and B. F. Only A. and C. G. Only A. and D. H. Only B. and C. I. Only B. and D. J. Only C. and D. K. Only A., B., and...
True or False With explanation please.
1- True or false: a. If A is an event of a sample space with P(A)-P(AS), then P(A)-0.5 b. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one P(A or B)-P(A)+P(B) P(A and B) P(A).P(B) by its own probability and then adding all the products together; that is P deviation of σ. If x is converted to the...
Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. IfE and F are complementary events, then E and F are mutually exclusive. Choose the correct answer below. O A. The statement is true because if E and F are complementary events, then EnF is equal to the sample space. B. The statement is false because the null set is an element of both E and F. Therefore, E and...
Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are complementary events, then E and F are mutually exclusive. Choose the correct answer below. A. The statement is true because two complementary events have to be mutually exclusive. B. The statement is true because if E and F are complementary events, then EnF is equal to the sample space. C. The statement is false because...
2. Let A and B be events in a sample space such that P(A) -0.5. P(ANB) -0.3 and PLAUB)=0.8. Calculate: 1) P(AB): ii) P(BA): iii) PIBIA B): be independent of A and such that B and Care Let the event C in mutually exclusive. Calculate: iv) P(AC); v) PIANBNC). (8 Marks)
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