F is an event, and
E1, E2, and E3
partition S.
P(E1) | = |
|
P(E2) | = |
|
P(E3) | = |
|
||||||
P(F | E1) | = |
|
P(F | E2) | = |
|
P(F | E3) | = |
|
Draw the tree diagram that represents the given information.
(a) Find
P(E1 ∩ F), P(E2 ∩ F), P(E3 ∩ F).
P(E1 ∩ F) = | |
P(E2 ∩ F) = | |
P(E3 ∩ F) = |
(b) Find
P(F).
P(F) =
(c) Find
P(E1 | F) and P(E3 | F).
P(E1 | F) = | |
P(E3 | F) = |
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points. The following probability assignments apply: p(E1 )=.05 p(E2)=.20 P(E3)=.20 p(E4)=.25 p(E5)=.15 p(E6)=.10 and p(E7)=.05 Let A={E1,E4,E6} B={E2,E4,E7} C= {E2,E3,E5,E7} 1) Find A ∩ B and P(A ∩ B) and Are events A and C mutually exclusive?
Suppose a sample space consists of five elementary outcomes e1, e2, e3, e4, e5with the characteristics that e1, e4, and e5are equally likely, e2is twice as likely ase1and e3is four times as likely as e1. a. DetermineP(ei) for i = 1, 2, ... 5 b. IfA = {e3, e4}, find P( A ).
Find the inverse of the elementary matrix E1 E2 E3 E4 and show the step 1 2 3 4
(5) In the circuit below, E1 11 V, E2 = 6 V, and E3 = 6 V. Also R1 26 a. R2 109 n, and R3 61 . Find the current through R1. E7 1. O 0.061 A 2.O 0.045 A 3. 0.026 A 4. O 0.034 A 5. O 0,083 A R2 E 3 E 1 W
2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3 such that E3E2E1A=I.
suppose that T:R^3 →R^2 is such that T(e1)= [ 2] T(e2)= [ 1 ] T(e3)=[ 0 ] [ 1 ] [ 1 ] [ 1] and suppose that S : R^2 → R ^2 is given by the projection onto the x axis (a) What is the matrix S◦ T? (b) What is the kernel of S◦T?
Let S be the tetrahedron in R3 with vertices at x the vectors 0, e1, e2, and e3, and let S' be the tetrahedron with vertices at vectors 0, v1, V2 and v3. See the figures to the right. Complete parts (a) and (b) below. a. Describe a linear transformation that maps S onto S lf T is a linear transformation that maps S onto S, then the standard matrix for T, written in terms of v1-v2, and v3, is...
Consider an experiment corresponding to the single throw of a die. Let E1 be the event that the throw is one of 11,2,3,4) and let E2 the event that the throw is one of 13,4,5,6). You are given that P(E) P(E2) 2/3. (a) Identify the smallest o-algebra sf containing the events E1 and E2. (b) Attach probabilities P(J) to all the elements J E (c) What can you say about the probability P(11]) of the event associated to a throw...
Thermodynamics 5. A system has three energy eigenstates (microstates), with energies 0, E1, and E2 » Ei. It is sitting in a heat bath (reservoir) with temperature T. a. Find the partition function Z(T). b. Find simple approximate expressions for Z when t > E2, E2 »T» Ei, and T < E1. For the high- and medium-temperature regimes, your expressions should be zeroth-order, i.e., should not contain t, but for the low-temperature regime you should include the leading T-dependence. c....
1) If the electron starts out in the ground state and is excited to level E3 by an incoming photon, what was the wavelength of that photon (in nm)? a) 95.4 nm b) 102.5nm c) 121.5nm d) 136.7 nm e) 182.3 nm 2) When the electron transitioned from E1 to E3 its orbital radius increased by a factor of: A) 1 (It didn’t change) B) 2 C) 3 D) 4 E) 9 3) What is the longest wavelength the hydrogen...