All forms of Bayes filters start with an initial belief. Choosing a uniform distribution as the initial belief shows the lack of knowledge about the state of the robot. Explain how you represent a uniform belief in each of the following Bayes filter implementations: (1) *discrete* Bayes filter: localizing a robot in a 1D world with 10 cells. (2) particle filter: localizing a robot using 50 particles (specify the initial weights of the particles, explain how do you initialize the particles). (3) (extended) Kalman filter: localizing a robot using (extended) Kalman filter (specify the initial mean and covariance matrix for Gaussian (Normal) belief). All forms of Bayes filters start with an initial belief. Choosing a uniform distribution as the initial belief shows the lack of knowledge about the state of the robot. Explain how you represent a uniform belief in each of the following Bayes filter implementations: (1) *discrete* Bayes filter: localizing a robot in a 1D world with 10 cells. (2) particle filter: localizing a robot using 50 particles (specify the initial weights of the particles, explain how do you initialize the particles). (3) (extended) Kalman filter: localizing a robot using (extended) Kalman filter (specify the initial mean and covariance matrix for Gaussian (Normal) belief)