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Question 1
Question-26. There are 5000 different color balls, out of which 1200 are pink color. What is the maximum likelihood estimate for the proportion of "pink" items in the test set of color balls?
Correct : C
In general, for a fixed set of data and underlying statistical model the method of maximum likelihood selects the set of values of the model parameters that maximizes the likelihood function. Intuitively, this maximizes the 'agreement' of the selected model with the observed data, and for discrete random variables it indeed maximizes the probability of the observed data under the resulting distribution. Maximum-likelihood estimation gives a unified approach to estimation, which is well-defined in the case of the normal distribution and many other problems. However in some complicated problems, difficulties do occur: in such problems, maximum-likelihood estimators are unsuitable or do not exist.
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Question 2
If E1 and E2 are two events, how do you represent the conditional probability given that E2 occurs given that E1 has occurred?
Correct : C
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Question 3
What is the probability that the total of two dice will be greater than 8, given that the first die is a 6?
Correct : B
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Question 4
A denote the event 'student is female' and let B denote the event 'student is French'. In a class of 100 students suppose 60 are French, and suppose that 10 of the French students are females. Find the probability that if I pick a French student, it will be a girl, that is, find P(A|B).
Correct : C
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Question 5
Which method is used to solve for coefficients bO, b1, ... bn in your linear regression model:
Correct : C
In the linear model, the bi's represent the unknown p parameters. The estimates for these unknown parameters are chosen so that, on average, the model provides a reasonable estimate of a person's income based on age and education. In other words, the fitted model should minimize the overall error between the linear model and the actual observations. Ordinary Least Squares (OLS) is a common technique to estimate the parameters
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