Question

In: Statistics and Probability

Let S = {s1, s2, s3, s4, s5, s6} be the sample space associated with an...

Let

S = {s₁, s₂, s₃, s₄, s₅, s₆}

be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If

A = {s₁, s₂}

and

B = {s₁, s₅, s₆},

find the following.

Outcome

Probability

s₁

s₂

s₃

s₄

s₅

s₆

(a)

P(A)

P(B)

(b)

P(A^C)

P(B^C)

(c)

P(A ∩ B)

(d)

P(A ∪ B)

(e)

P(A^C ∩ B^C)

(f)

P(A^C ∪ B^C)

Solutions

Expert Solution

s1	1/3
s2	1/7
s3	1/6
s4	1/6
s5	1/21
s6	1/7

A =	{s1, s2}	3456
B =	{s1, s5, s6}	234

a) P(A) =	P(s1) + P(s2) =	1/3 + 1/7 =	10/21
b) P(B) =	P(s1) + P(s5) +P(s6) =	1/3 + 1/21 + 1/7 =	11/21
c) P(Ac) =	1 - P(A)	1 - 10/21 =	11/21
d) P(Bc) =	1 - P(B)	1 - 11/21 =	10/21
e) P(A and B) =	P(s1)	1/3	1/3
f) P(A or B) =	P(s1) + P(s2) + P(s5) + P(s6)	1/3 + 1/7+1/21 + 1/7 = 14/21	2/3
g) P(Ac and Bc) =	P(A or B)c = 1 - P(A or B)	1 - 2/3	1/3
h) P(Ac or Bc) =	P(A and B)c = 1 - P(A and B)	1 - 1/3	2/3

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Consider the following spot rate curve: s1 s2 s3 s4 s5 0.050 0.055 0.061 0.066 0.075...

Consider the following spot rate curve: s1 s2 s3 s4 s5 0.050 0.055 0.061 0.066 0.075 (a) What is the forward interest rate that applies from period 3 to period 5? That is, what is the value of f3,5? Assume annual compounding. (Keep your answer to 4 decimal places, e.g. 0.1234.) (b) If the market forward rate from period 3 to period 5 is not equal to the value derived in (a), how can you create an arbitrage opportunity? (No...

Let S = (s1, s2, . . . , sn) be a given sequence of integer...

Let S = (s1, s2, . . . , sn) be a given sequence of integer numbers. The numbers can be positive or negative. We define a slice of S as a sub- sequence (si,si+1,...,sj) where 1 ≤ i < j ≤ n. The weight of a slice is defined as the sum of its elements. Provide efficient algorithms to answer each of the following questions: a)Is there any slice with zero weight ? b)Find the maximum weight slice in...

Consider three inertial frames S1, S2 and S3, all moving in the y-direction. S3 moves w.r.t...

Consider three inertial frames S1, S2 and S3, all moving in the y-direction. S3 moves w.r.t S1 at a speed v31 = 0.35c and at v32 = −0.53c w.r.t S2. 1. What is the velocity of S2 as measured by observers in S1? 2. A meter stick at rest in S3 is tilted at an angle of θ3 = 30◦ to the y axis. How long is the meter stick, and what angles θ1 and θ2 does it make with...

F=xyi+yzj+zk. LetSbe the boundary of the cylinder 0≤z≤1,x2+y2≤1 (oriented outwards), andEthe interior. Compute∫∫S(F)·dSdirectly (S=S1+S2+S3, withS1=top,S3=bottom,S2=side. OnS1andS3you...

F=xyi+yzj+zk. LetSbe the boundary of the cylinder 0≤z≤1,x2+y2≤1 (oriented outwards), andEthe interior. Compute∫∫S(F)·dSdirectly (S=S1+S2+S3, withS1=top,S3=bottom,S2=side. OnS1andS3you can just say what dS is, but you must compute on S2.

Motorcade Company has three service departments (S1, S2, and S3) and two production departments (P1 and...

Motorcade Company has three service departments (S1, S2, and S3) and two production departments (P1 and P2). The following data relate to Motorcade's allocation of service department costs: Round to two decimal places. Budgeted Costs Nbr of Employees S1 $3,120,000 75 S2 2,060,000 50 S3 1,000,000 25 P1 150 P2 225 Service department costs are allocated by the direct method. The number of employees is used as the allocation base for all service department costs Calculate the total service department...

Let S1 and S2 be any two equivalence relations on some set A, where A ≠...

Let S1 and S2 be any two equivalence relations on some set A, where A ≠ ∅. Recall that S1 and S2 are each a subset of A×A. Prove or disprove (all three): The relation S defined by S=S1∪S2 is (a) reflexive (b) symmetric (c) transitive

SUPPLIER Sno Sname Status City s1 Smith 20 London s2 Jones 10 Paris s3 Blake 30...

SUPPLIER Sno Sname Status City s1 Smith 20 London s2 Jones 10 Paris s3 Blake 30 Paris s4 Clark 20 London s5 Adams 30 NULL PART Pno Pname Color Weight City p1 Nut Red 12 London p2 Bolt Green 17 Paris p3 Screw NULL 17 Rome p4 Screw Red 14 London p5 Cam Blue 12 Paris p6 Cog Red 19 London SHIPMENT Sno Pno Qty Price s1 p1 300 .005 s1 p2 200 .009 s1 p3 400 .004 s1 p4...

Write each vector as a linear combination of the vectors in S. (Use s1 and s2,...

Write each vector as a linear combination of the vectors in S. (Use s1 and s2, respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.) S = {(1, 2, −2), (2, −1, 1)} (a) z = (−8, −1, 1) z = (b) v = (−2, −5, 5) v = (c) w = (1, −23, 23) w = (d) u = (2, −6, −6) u =

Write each vector as a linear combination of the vectors in S. (Use s1 and s2,...

Write each vector as a linear combination of the vectors in S. (Use s1 and s2, respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.) S = {(1, 2, −2), (2, −1, 1)} (a) z = (−13, −1, 1) z = (b) v = (−1, −5, 5) v = (c) w = (−2, −14, 14) w = (d) u = (1, −4, −4) u =

Find the inverse Laplace transform of a. F(s) = se-6s/(s-2)(s2+2s+1) b. F(s) = e-12s/s3(s2+4)

Subjects