2.2.28
(a) Ac = { x ; x=0 or 5x10 }
(b) AB = { x ; 3x5 }
(c) AB = { x : 0x7 }
(d) Bc = { x : 0x3 or 7x10 } ABc = { x : 0<x<3 }
(e) AcB = { x : x=0 or 3x10 }
(f) AcBc = { x : x=0 or 7x10 }
2.4.8
P(AB) = P(A) + P(B) - P(AB)
P(AB) 1 P(A) + P(B) - P(AB) 1 P(A) + P(B) - 1 P(AB) P(AB) a+b-1
P(A|B) = P(AB)/P(B)
P(AB) a+b-1 P(AB)/P(B) (a+b-1)/P(B) P(A|B) (a+b-1)/b
PROVED
2.4.50
P(1 is sent) = 0.7 P(0 is sent) = 0.3
P(0 is received | 0 is sent) = 0.9 P(1 is received | 0 is sent) = 0.1
P(1 is received | 1 is sent) = 0.95 P(0 is received | 1 is sent) = 0.05
Required Probability = P(0 is sent | 1 is received)
According to Bayes theorem of conditional probability :-
2.2.28 2.4.8 2.4.50 five (a) AUB-B 80f (1) AnB=A et B five 2.2.28. Let events A...
1 Let A and B be independent events with P(A) and P(B) = FICE Find P(ANB) and P(AUB). 8 P(ANB) = P(AUB) =
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)
Let S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16). A= {1,3,5,7,9) B= {1,2,4,5,6,9} C= {2,6,9,10,12,14} Find: (1) (AUB) (3) (COB) (2) (ANB) (5) (ANBNC) (4) AC
-/11.11 points s may Noves not your rescher v Let A and B be two events in a sample space for which Pr(A) - 2/3, Pr(B) - 1/6 and Pr[AnB) - 1/9 a. What is Pr(AUB)? b. What is Pr(AB)? c. What is Pr(BIA)? d. What is Pr )? e. What is Pr(A)? f. What is Pr(B)? 9. What is Pr(CAU B)')?
1. Javier volunteers in community events each month. He does not do more than five events in amonth. He attends exactly five events 35%ofthetime, four events. 2596-ofthetime, three events.20% of the time, two events-10% of the time, oneevent 596 of the time, and no events 5% ofthe-time. - a. Define the random variable X. many events avier valanicers far n a b. What values does x take on? / J c. Construct a PDF table. d. Find the probability that...
Problem #3: Let A and B be two events on the sample space S. Then show that a. P(B) P(AOB)+P(AnB) b. If Bc A, then show that P(A)2 P(B) Show that P(A| B)=1-P(A|B) C. P(A) d. If A and B are mutually exclusive events then show that P(A| AUB) = PA)+P(B) Problem 4: If A and B are independent events then show that A and B are independent. If A and B are independent then show that A and B...
f(x) = p* (1 – p)1-*, x = 0,1, Osp s 1. a) For a sample of size n drawn from this distribution write the likelihood function and compute the formula for the maximum likelihood estimate (MLE), P. b) Show that p is unbiased and compute the variance of p. Is consistent? c) Five tosses a coin showed the following outcomes: HHHHH. Compute the MLE of p=Pr(H). What do you conclude about the coin? d) The frequency of H in...
Problem o.1 Let X, be the number of people who enter a bank by time t > 0. Suppose k! for k- 0,1,2,..., and s (t - s)k-e-t for t>s> 0, and k2r 0,1,2,.... (a) Find Pr[X2 k| X 1 for k 0,1,2,.... (b) Find E2 X1 1 Useful information: Don't eat yellow snow, andeot/k! Problem o.2 Recall the Geometric(p) distribution where X- number of flips of a coin until you get a head (H) with Pr(H) - p. The...
Let a, b, c, d and e be the first five digits of your La Trobe student number. i.e. if your student number is 12345678 then a = 1,b=2,c=3, d = 4 and e = 5. Use your appropriate values in the question below. 2 a Consider the line. L = {(2,3, 2): ?- } y-b 3 2 (a) Write L in parametric form. (b)0 Find the coordinates of the point P at which L intersects the plane z =...
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...