Conditional Probability
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Conditional Probability
How can I calculate P(A) and P(B) from P(C), P(C'), P(AlC), and P(BlC)?
How do I calculate P(A) and P(B) independence?
Step by step
Solved in 3 steps
- Draw the probability tree for the situation. Draw the reverse tree for the situation.Simulate a probability curve fx (x)~N(µ,δ) in Matlab AND Calculate the cumulative probability fx(x) Note: you are free to choose the example or the data for your case study.What is conditional probability? If we know that P (A) = 1/4, that P(B) = 1/2, and that P(B|A) = 1/2, what is P (A|B) ? %3D
- Simulate a probability curve fx(x)~N(µ,δ) in Matlab AND Calculate the cumulative probability fx (x)note: attach matlab code of the simulation, may be in text1. The impulse response of a causal system is: h(t) = A cos(wt) e¯¹/¹u(t) where u(t) is the Heaviside step function. The response is measured experimentally with a sampling interval of T. a. Write an expression for the sampled impulse response h[n]. b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tables provided below as necessary. c. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer. d. What is the DC gain of H[z]? e. Write a difference equation that describes the output y[n] in terms of input x[n].The following MDP world consists of 5 states and 3 actions: (1, 1) (1, 2) Action: Exit - -10 Actions: down, right (2, 1) (2, 2) Action: Exit = -10 Actions: down, right (3, 1) Action: Exit = 10 When taking action down, it is successful with probability 0.7. with probability 0.2 you go right, and with probability 0.1 you stay in place. When taking action right, it is successful with probability 0.7, with probability 0.2 you go right, and with probability O.1 you stay in place. When taking action Exit, it is successful with probability 1.0. The only reward is when taking action Exit, and there is no discounting. Calculate the value of states using Value Iteration algorithm for required time step: Provide the value for State (1,2) at time step 4 (calculate to 3 decimal places): Va(1,2) =
- 2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.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 probabilityA and B are events, neither of which has probability 0. Which conditions below imply that A and B are independent events? Select all that apply. Select 3 correct answer(s) 0 0 0 0 S SO p(AB) = p(BA) p(BA) = p(B) p(An B) =p(A) × p(B) p(BA) = p(A) x p(B) p(An B) = p(AB) p(AB) = P(A) p(AB) = p(B) p(BA) = P(A) P(AB) = P(A) x p(B) 0/1 point
- nd the python file about the probability road map. Read the code and make an attempt to comprehend what is occurring. Emphasis will be placed on graph formation and the Dijkstra method. Modify the following variables in probabilistic road map. py:N_SAMPLE = 500N_KNN = 10 MAX EDGE LEN = 30.0 but plz use python. ThanksA unigram is a sequence of words of length one (i.e. a single word).• A bigram is a sequence of words of length two.• The conditional probability of an event E2 given another event E1, written p(E2|E1), is the probability that E2 will occur given that event E1 has already occurred.We write p(w(k)|w(k-1)) for the conditional probability of a word w in position k, w(k), given the immediately preceding word, w(k-1). You determine the conditional probabilities by determining unigram counts (the number of times each word appears, written c(w(k)), bigram counts (the number of times each pair of words appears, written c(w(k-1) w(k)), and then dividing each bigram count by the unigram count of the first word in the bigram:p(WORD(k)|WORD(k-1)) = c(WORD(k-1) WORD(k)) / c(WORD(k-1)) Apply and incorporate instrutions to code below. #include <stdio.h>//including headers#include <string.h>#include <stdlib.h> struct node{//structure intialization int data; struct node *next; };…In the theoretical landscape of probability theory, a multifaceted inquiry unfolds: Can we dissect the complexities of stochastic processes and their role in modeling dynamic systems over time? How do concepts like Markov chains and Brownian motion contribute to understanding the evolution of random phenomena, transcending mere chance into a nuanced exploration of theoretical probabilities with real-world implications? Furthermore, how does the convergence of these theoretical frameworks amplify our ability to analyze and predict the uncertain trajectories of diverse phenomena in fields ranging from finance to physics?