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5. Consider an experiment with sample space S and events A,B,C, and D with the following...
Consider an experiment with sample space S and events A,B,C, and D with the following probabl...
Consider an experiment with sample space S and events A,B,C, and D with the following probabl ities: P(AUB)-, P(A)- , P(Cn D) , PC)- . Furthermore, A and B are mutually exclusive (i.e. AnB-), while C and D are independent (i.e. P(CND) P(C)P(D)). Note: I know this looks like a lot of parts, but these are all short, quick answers!) ' (a) Find P(AnB (b) Find P(B) (c) Find P(A กั Bc). (d) Find P(AUBe) (e) Are A and B...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to your phone bounces off numerous obstacles, causing multiple copies of the transmitted signal with different delays to arrive at your phone. These copies can add constructively or destructively, resulting in an effect called "multipath fading". The simplest (and perhaps most common) model for such is Rayleigh fading, which is a consequence of the (celebrated) Central Limit Theorem that we will learn later in the...
In a sample space, events A and B are independent, events B and C are mutually...
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
(d) It is bimodal. (3) What is the set of all simple events of an experiment...
(d) It is bimodal. (3) What is the set of all simple events of an experiment called (a) a population (b) a distribution (e) a sample space (d) a random sample (4) For two events A and B. suppose: A 03 0.4 Then PiAU B) is equal to A0.1 0.2 (5) Suppose PA).4. P B) 0.3, and P(AnB) o.12. Which one of the following statements correctly defines the relationship hetween events A and B (a) Events A and B are...
#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 A, B and C be events in the sample space S. Use Venn Diagrams...
1. Let A, B and C be events in the sample space S. Use Venn Diagrams to shade the areas representing the following events (32 points) a. AU (ANB) b. (ANB) U ( AB) C. AU ( ANB) d. (AUB) N (AUC)
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)
3. Let A, B, C be events in a sample space S. Prove that (a) P(AUB)...
3. Let A, B, C be events in a sample space S. Prove that (a) P(AUB) P(A)P(B), (b) P(AUBUC) P(A)+P(B)+P(C)-P(AnB)-P(Anc)-P(Bnc)+P(AnBnc)
05 (24 marks) Let A, B, and C be three events in the sample space S....
05 (24 marks) Let A, B, and C be three events in the sample space S. Suppose we know that A U B U C-S, P(A)-1/2, P(B)-1/3, PALJ B-3/4. Answer the following questions: a) Find P(AnB). (4 marks) b) Do A, B, and C form a partition of S? Why? (4 marks) c) Find P(C-(AUB)). (8 marks) d) If P(Cn (AU B))-5/12, find P(C). (8 marks)
Let and B be events in a sample space S, and let C = S -...
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
Consider an experiment with sample space S and events A,B,C, and D with the following probabl ities: P(AUB)-, P(A)- , P(Cn D) , PC)- . Furthermore, A and B are mutually exclusive (i.e. AnB-), while C and D are independent (i.e. P(CND) P(C)P(D)). Note: I know this looks like a lot of parts, but these are all short, quick answers!) ' (a) Find P(AnB (b) Find P(B) (c) Find P(A กั Bc). (d) Find P(AUBe) (e) Are A and B...
4. Wireless Communications: Background: Per recitation, a wireless communication signal traveling from a cellphone tower to your phone bounces off numerous obstacles, causing multiple copies of the transmitted signal with different delays to arrive at your phone. These copies can add constructively or destructively, resulting in an effect called "multipath fading". The simplest (and perhaps most common) model for such is Rayleigh fading, which is a consequence of the (celebrated) Central Limit Theorem that we will learn later in the...
(d) It is bimodal. (3) What is the set of all simple events of an experiment called (a) a population (b) a distribution (e) a sample space (d) a random sample (4) For two events A and B. suppose: A 03 0.4 Then PiAU B) is equal to A0.1 0.2 (5) Suppose PA).4. P B) 0.3, and P(AnB) o.12. Which one of the following statements correctly defines the relationship hetween events A and B (a) Events A and B are...
#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 A, B and C be events in the sample space S. Use Venn Diagrams to shade the areas representing the following events (32 points) a. AU (ANB) b. (ANB) U ( AB) C. AU ( ANB) d. (AUB) N (AUC)
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)
3. Let A, B, C be events in a sample space S. Prove that (a) P(AUB) P(A)P(B), (b) P(AUBUC) P(A)+P(B)+P(C)-P(AnB)-P(Anc)-P(Bnc)+P(AnBnc)
05 (24 marks) Let A, B, and C be three events in the sample space S. Suppose we know that A U B U C-S, P(A)-1/2, P(B)-1/3, PALJ B-3/4. Answer the following questions: a) Find P(AnB). (4 marks) b) Do A, B, and C form a partition of S? Why? (4 marks) c) Find P(C-(AUB)). (8 marks) d) If P(Cn (AU B))-5/12, find P(C). (8 marks)
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
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