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I want help to solve this question (6) Suppose that PCB An) = – and that...
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(4) (a) Suppose that P(A) = P(B) = ? and that P(A|B) = P(B). Calculate P( AB') (b) Suppose that P(ANB) = , P(A|B') = and P(B) = . Calculate P(A) (c) Let A and B be events such that P(A) = if BCA and P(B']A) = Calculate P(B)
Question 4 Suppose that P(BA) = and that P(B|A2 , where A1 and Az are two equally likely events forming a partition of S. Calculate P (A, B)? O a. 1
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10) Prove the following a+b-1 b (a) Let P(A) = a and P(B) = b then P(A|B) 2 a+b=1 (b) If A1, A2, -. , An is a sequence of independent events, then ) = 1 - [1 - P(A1)]. [1 – P(A2)]... [1 - P(An)] n i=1
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Stat 352 Homework Set 2 Fall 2019: Conditional Probability and Independence Deadline: Monday November 11, 2019 (1) In throwing two dice with the sample space Define the following events on : = {(x,y):x, y = 1,2,3,4,5,6). A = {sum less than 4) = {(x, y): x + y < 4, x, y = 1,2,3,4,5,6) B = {first number is 1) = {(x,y): x = 1, y = 1,2,3,4,5,6) C = {sum of number is...
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(3) A fair die is rolled twice, independently. (a) Consider the events: A = "the first number that show up is a 6"| B = "the sum of the two numbers obtained is equal to 7" C=" the sum of the two numbers obtained is equal to 7 or 11“ (i) Calculate P(BIC) (ii) Calculate P(A|B) (iii) Are A and B independent events? (b) Considering rolling two dice. Knowing that an even number...
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(9) A device is composed of two components, A and B, subject to random failures. The components are connected in parallel and, consequently, the device is down only if both components are down. The two components are not independent. We estimate that the probability of a failure of component A is equal to 0.2; a failure of component B is equal to 0.8 if component A...
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Stat 352 Homework Set 2 Fall 2019: Conditional Probability and Independence Deadline: Monday November 11, 2019 (1) In throwing two dice with the sample space Define the following events on : 1,2,3,4, 5,6}. {(x, y): x, y = A={sum less than 4) {(x, y): x + y < 4, x,y = 1,2,3,4,5,6} first number is 1) = {(x, y): x = 1, C = {sum of number is 5} = {(x, y): x...
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A system is made up of three independent components. It operates if at least two of the three components operate. If the reliability of each component is equal to 0.95, what is the reliability of the system?
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The barometric pressure depends on the altitude above the level of the sea. The following measures have been taken. h (Km) 0.51 1.52 2.5 3 3.5 p (KPa) 101.32 95.15 89.36 83.93 7882 74.02 69.52 65.29 61.32 4 a. Verify that the function describing the pressure as a function of the altitude is following an exponential model. b. Find an expression for p(h) using the form Ab Calculate the barometric...
Hi! This question has 6 parts to it. I completed parts 1-3 but need help with 4-6. For 1, I got D (755 + .65Yd), 2: 2055, and 3: B (C = 940 + .65 Yd). Are these correct thus far? 1. Suppose the consumption function is: C = a1 Yd + a2 WRE/S + a3CC Where all the a’s (the sensitivity parameters) are greater than zero. Initial conditions: Let a1 = 0.65, a2 = 0.04, a3 = 0.5, WRE/S...