Question

Write TRUE or FALSE in front of each of the following statements. If the question is false, correct the statement. Each question is worth 2 points. 1. (2) Leave-one-out cross validation (LOOCV) is more computationally expensive than the validation set approach. 2. (2) In general, when regression models are trained on fewer observations, the test error may be overestimated (i.e., it may be lower than it actually is) 3. (2) Repeated measures are reflected as fixed effects in regression models. 4. (2) Multivariate statistics is able to analyze data in which there are many independent and dependent variables, all correlated with one another 5. (2) In the Bayesian paradigm, the probability of an event is equal to the long-term frequency of the event's occurrence when the same process is repeated many times 6. (2) In Bayesian statistics, we have to make assumptions about the underlying distribution of data before performing any analyses. 7. (2) In frequentist statisticiss, we can tiē probabilities to hypotheseses statements. 8. (2) A benefit of Bayesian statistics is that it can incorporate prior beliefs and prior knowledge into decisions and we can update our beliefs with new data 9. (2) The data (Y) are fixed in Bayesian statistics and the parameters (θ) are fixed in frequentist statistics. 10. (2) When the posterior and prior distributions come from the same family, they are called conjugate distributions.

Answer 1

Answer: True

Explanation:

(i) Given P={m,n} and Q={n,m} then

P×Q={(m,n),(m,m),(n,n),(n,m)}

So, given value of P×Q is incorrect.

Hence, the given statement (i) is false.

(ii) If A and B are non-empty sets, then A×B is a non-empty set of ordered pairs (x,y) such that x∈A and y∈B

Hence, the given statement (ii) is true.

(iii) A={1,2} and B={3,4}

A×(B∩ϕ)=A×ϕ=ϕ

So, (iii) is true.