Given the following Bayesian network, where all random variables have Boolean values (true or fal...
17. Consider the Bayesian network drawn below A P(A true) 0.4 P(B-true | A-false)0.9 D P(B-true | A-true0.3 P(C-true) 0.7 P(D true | B-false and C-false)0.8 P(D-true | B-false and C-true) 0.3 P(D-true | B-true and C-false) 0.5 P(D-true | B-true and C-true)0.1 Show your work for the following calculations a) Compute P(A true and B -false and C- true and D -false) b) Compute P(D true | A -false and B-true and C-false) cCompute P(A true | B -false...
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. A B C x P(x) x P(x) x P(x) 25 0.2 25 0.2 25 0.2 50 0.4 50 0.4 50 0.4 75 0.1 75 0.1 75 0.1 100 0.3 100 0.5 100 0.7 a. Which of the above tables is a probability distribution? b. Using the correct probability distribution, find the probability that x is: (Round the final answers to...
The discrete random variables ? and ? have joint probability function ?, where ? is given by the following table: X 1 2 3 4 1 0.1 0.2 0.1 0.05 Y 2 0.05 0 0.1 0.1 3 0 0.2 0.05 0.05 a) Determine ?(1 < ? ≤ 3, 1 ≤ ? ≤ 2). [4 marks] b) Calculate ?(?^2 ?). [4 marks] c) Find the marginal probability functions ? and ℎ of ? and ? respectively. [4 marks] d) Are ?...
Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. 25 0. 50 0.7 75 0.2 100 0.4 25 -0.6 25 0.5 50 0.2 50 0.3 75 100 0.1 100 0.1 0.1 75 01 a. Which of the above tables is a probability distribution? b. Using the correct probability distribution, find the probability that xis: (Round the final answers to 1 decimal place.) 1. Exactly 75- 2. No more than...
4. Basic Computation: Addition Rule Given P(A) = 0.7 and P(B) = 0,4 (a) Can events A and B be mutually exclusive? Explain. | (b) If P(A and B) = 0.2, compute P(A or B). 3. Basic Computation: Multiplication Rule Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(AIB) = 0.1, compute P(A and B). 6. Basic Computation: Multiplicat (a) If A and B, are independent...
= 0.3. Consider events A and B such that P(A) = 0.7, P(B) = 0.2 and P(ANB) Compute the probability that A will occur, given that B does not occur, A. 0.4 B. 0.1 C. -0.1 D. 0.5 E. none of the preceding
Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The joint probability mass function of these two random variables are given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15 0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions fX1 (s) and fX2 (t). b. What is the expected values of X1...
Two fuzzy as follow sets A,B defined on the universe X={0,1,2,3,4,5,6,7,8,9} A 0.1/1, 0.2/2, 0.6/3, 1/4, 0.5/5,0.3/6, 0.2/7, 0.1/8} B 0.2/1, 0.3/2, 0.6/3,1/4, 0.7/5, 0.4/6, 0.3/7, 0.2/8, 0.1/9 Answer the following questions: (I)Sketch the membership functions of A and B sets (ii Compute and sketch C=AOB & D=AUB; (iii) Is the following relation true/false? Please clarify ACB Two fuzzy as follow sets A,B defined on the universe X={0,1,2,3,4,5,6,7,8,9} A 0.1/1, 0.2/2, 0.6/3, 1/4, 0.5/5,0.3/6, 0.2/7, 0.1/8} B 0.2/1, 0.3/2, 0.6/3,1/4,...
1) Suppose that three random variables, X, Y, and Z have a continuous joint probability density function f(x, y. z) elsewhere a) Determine the value of the constant b) Find the marginal joint p. d. fof X and Y, namely f(x, y) (3 Points) c) Using part b), compute the conditional probability of Z given X and Y. That is, find f (Z I x y) d) Using the result from part c), compute P(Z<0.5 x - 3 Points) 2...