(b) 1 2 3 4 P(X=x) 1 1 1 9. - 4 8 16 16
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- A confusion matrix based on one particular cut-off probability can determine the entire ROC curve. True FalseUsing the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.True or False: The probability a continuous random variable is near some value is defined by its probability density function. True False
- Discrete Probability: Make sure to solve the problem correctly and show the correct solution.If 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
- Question: Briefly explain joint and marginal probability.For a HMM, the hidden states are {bull, bear}, the observation variables are {rise, fall}, the initial state probability distribution is [0.5 0.5]¹, the transition probability distribution A is [0.4 0.7; 0.6 0.3], and the observation probability distribution B is [0.8 0.1;0.2 0.9]. If the observation sequence is {fall fall rise}, please show the computation procedure for estimating the most likely state sequence?Draw the probability tree for the situation. Draw the reverse tree for the situation.
- 3 Using Receiving Operating Characteristic (ROC) evaluate a binary classifier and various probability thresholds. Note: Use JupyterNotebook.Assume that, with probability 0.8, It’s going to snow and/or I’m going to stay at home; and with probability 0.7, when it snows, then I stay at home. What is the probability of being truth that I am going to stay at home?Given access to a robot's motion model and prior belief distribution, how can we compute the probability P(x|u) where x is the latest robot's state and u is the control applied at a previous state x'?