we know that P(A) = 1/4, that P(B) = 1/2, ar P(B|A) = 1/2, what is P(A|B) ? and that
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A: Below is the detailed python code for the given problem statement:
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A: Here is the detailed python code for the given problem statement:
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- The random variable X and Y are independent. The random variable X has the probability distribution P(X=0) = 0.4 and P(X=1) = 0.6. The random variable Y has the probability %3D distribution P(Y=0) = 0.2 and P(Y=3) = 0.8. Fill the following Joint distribution table: Y P(X,Y) 3 1 1 Note: round your answer to decimal places.Probability Consider a probability experiment with S = {0, 1, 2, 3, 4, 5, 6, 7} and these two events: A = {1,2, 3}, and B= {1,3, 5, 6, 7} What is the probability that A occurs? What is the probability that B occurs? What is the obability that A n B occurs? What is the probability that AU Boccurs? What is the probability that {} occurs? What is the probability that S occurs?In a joint probability distribution table for 4 variables (A, B, C, D), how many entries will there be? 4 8 16 32
- You are given the following data: vocabulary V = (w1, w2, w3) and the bigram probability distribution p on V x V given by: !! p(w1, w1) = p(w3, w3) = 1/5 %3D p(w2, w2) = 0, !3! p(w2, w1) = 1/6, !3! p(w1, w3) = 1/5, %3D p(w2,w3)=1/15 p(w1, ") = 2/5 (that is w1 as the first of a pair). p(*, w2) = 1 /6. %3! Calculate p(w1, w2) and p(w2 | w3) using Markov's rule9. Prove the formula: e* ≥ 1 + x, Vx € R. 10. What is the probability that in a random group of 10 people at least two have the same birthday? Consider the experiment: Two fair die are cast and the sum of the spots shown on the uppermostThe sample space of a random experiment is (a, b, c, d, e, f, and each outcome is equally likely. A random variable is defined as follows: outcome X с d TEISEER 1.5 1.5 a b 0 2 Determine the probability mass function of X. Use the proba- bility mass function to determine the following probabilities: (a) P(X= 1.5) (b) P(0.5 3) (d) P(0 ≤X<2) (e) P(X=0 or X = 2)
- Give an example of a random variable X : {b, c, d, e} → N (Natural Number) with expectation 2, where each of {b, c, d, e} has equal probabilityIf the probability of an event is 62%, what is the probability of its complement?Let X and Y be two binary, discrete random variables with the following joint probability mass functions. (a) Compute P(X = 0]Y = 1). (b) Show that X and Y are not statistically independent. P(X = 0, y = 1) = P(X = 1, Y = 0) = 3/8 P(X = 0, y = 0) = P(X = 1, Y = 1) = 1/8
- For a given joint probability distribution f (x, y) where 0 < x < 4 and 0 < y < 5, which of the following equation provides the marginal probability of y? O f f (x, y) dy O S f (x, y) dx S f (x, y) dx O sf f (x, y) dæConsider the joint probability distribution on the right.a) What is P(A = false)? Show your work.b) What is P(A=true or B=true)? Explain.c) What is P(A=true|C=false)?d) Are A and C independent? Why?Given 2 patterns at 0.4 and 0.6, estimate probability density analytically using a rectangular window of width 0.3, using a triangular window of width 0.3 and using 1 nearest-neighbour.