1. Which of the following random variables are the default model for random samples?
a) iid
b) id
c) pmd
d) all of the mentioned
Explanation: Random variables are said to be iid if they are independent and identically distributed.
2. Cumulative distribution functions are used to specify the distribution of multivariate random variables.
a) True
b) False
Explanation: In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x.
3. Point out the correct statement.
a) The exponent of a normally distributed random variables follows what is called the log-normal distribution
b) Sums of normally distributed random variables are again normally distributed even if the variables are dependent
c) The square of a standard normal random variable follows what is called chi-squared distribution
d) All of the mentioned
Explanation: Many random variables, properly normalized, limit to a normal distribution.
4. Which of the following is incorrect with respect to use of Poisson distribution?
a) Modeling event/time data
b) Modeling bounded count data
c) Modeling contingency tables
d) All of the mentioned
Explanation: Poisson distribution is used for modeling unbounded count data.
5. __________ random variables are used to model rates.
a) Empirical
b) Binomial
c) Poisson
d) All of the mentioned
Explanation: Poisson distribution is used to model counts.
6. Point out the wrong statement.
a) The normal distribution is asymmetric and peaked about its mode
b) A constant times a normally distributed random variable is also normally distributed
c) Sample means of normally distributed random variables are again normally distributed
d) None of the mentioned
Explanation: The normal distribution is symmetric and peaked about its mean.
7. Which of the following form the basis for frequency interpretation of probabilities?
a) Asymptotics
b) Symptotics
c) Asymmetry
d) All of the mentioned
Explanation: Asymptotics is the term for the behavior of statistics as the sample size.
8. Bernoulli random variables take (only) the values 1 and 0.
a) True
b) False
Explanation: The Bernoulli distribution arises as the result of a binary outcome.
9. The _________ basically states that the sample mean is consistent.
a) LAN
b) LLN
c) LWN
d) None of the mentioned
Explanation: LLN stands for law of large numbers.
10. Which of the following theorem states that the distribution of averages of iid variables, properly normalized, becomes that of a standard normal as the sample size increases?
a) Central Limit Theorem
b) Central Mean Theorem
c) Centroid Limit Theorem
d) All of the mentioned
Explanation: The Central Limit Theorem (CLT) is one of the most important theorems in statistics.