фил 1. let A and B be events. with P(A1=1/2₁ P (B) = 1/3 and P(ANB) = /p. Find ÿ (A/B) W) P (B/A) ü/P(AUB)) y (1) P (A/B) UP (BIA)
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- If A and B are events for which P(A U B) = 1,then P(A' U B') = a) 1 b) Р(А') + P(В") c) P(A) + P(Β') - 1 d) 0 e) P(A') + P(B') – P(A') · P(B')The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?
- Assume that M= N(h)+k, h² + k, h* + ... Use the following data to find N,(). N,(h)=2.451, N,G)=2.896, N,)=3.285, N,(- = 3.786, N,()= 4.422 16 O a. 4.634 O b. 4.287 O c. 3.044 O d. 3.4146 O e. 3.953 O f. 5.058 Og. 3.674Let S. be the time it takes a standard Brownian motion to hit a. Find the probabilities 1) P(S2 < S_4), 1) P(S < S_2 < S4), 2) P(S1 < S_2 < S1 < S12).1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…
- Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].(b) Let X~N(40,144) and if Y = 2X – 1 Find the following probabilities: (i) P(X 50) (iii)P(35 < X < 45),(iv)P(-45 < Y < 45).(v)P(-50 < Y < 100)
- the second photo is an example of resolutionCalculate the following probabilities. a) If X,X-NID(-0,0¹), what is approximate value of Pr(-Sa')? e) If X₁ X₂X₁-Noa), K.,.,- N(0,0)), and Xs and Ys are independent, what T (L.) is Pr X₁-X oxA student goes to the library. Let events B=B= the student checks out a book and D=D= the student check out a DVD. Suppose that P(B)=0.59PB=0.59, P(D)=0.45PD=0.45 and P(D|B)=0.50PD|B=0.50. Round each answer to four decimal places. Find P(B′) Find P ( D and B) Find P (B\D) Find P (D and B') Find P (D\B')