Question

1. Consider the problem discussed in the class about learning a generative model for a discrete random variable which emulates a coin toss. Modeling the random variable as a Bernoulli distribution with theta indicating the probability of observing a head, answer the following questions: a) For D = {H,T,H,H,H} and using the MLE approach, the probability of observing a heads will be 0.5. b) For D = {H,T,H,H,H} and a Beta(0.5,0.5) prior, the probability of heads using the MAP estimate is 0.5. c) The MLE for theta using D = {H,H,H,T,H} will be higher than using D = {T,H,H,H,H} d) For D = {H,T,H,H,H} and using the MLE approach, the probability of observing a tails will be 0.2.

          1. Consider the problem discussed in the class about learning a generative model for a discrete random variable which emulates a coin toss. Modeling the random variable as a Bernoulli distribution with theta indicating the probability of observing a head, answer the following questions:
a) For D = {H,T,H,H,H} and using the MLE approach, the probability of observing a heads will be 0.5.
b) For D = {H,T,H,H,H} and a Beta(0.5,0.5) prior, the probability of heads using the MAP estimate is 0.5.
c) The MLE for theta using D = {H,H,H,T,H} will be higher than using D = {T,H,H,H,H}
d) For D = {H,T,H,H,H} and using the MLE approach, the probability of observing a tails will be 0.2.

1. Consider the problem discussed in the class about learning a generative model for a discrete random variable which emulates a coin toss. Modeling the random variable as a Bernoulli distribution with theta indicating the probability of observing a head, answer the following questions:
a) For D = H,T,H,H,H and using the MLE approach, the probability of observing a heads will be 0.5.
b) For D = H,T,H,H,H and a Beta(0.5,0.5) prior, the probability of heads using the MAP estimate is 0.5.
c) The MLE for theta using D = H,H,H,T,H will be higher than using D = T,H,H,H,H
d) For D = H,T,H,H,H and using the MLE approach, the probability of observing a tails will be 0.2.

Added by David H.

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