13

Question 1

A collection of random variables are independent if?

Answer 1

We pick any subset of RV and if we ask what is the probability that the first one is less and equal to some number and/or another one is less and equal to some other number, then its essentially a product of the individual probabilities.

Question 2

Collection of random variables are identically distributed if?

Answer 2

If the cumulative distribution of one random variable is equal to the cumulative distribution of the other random variable. This means that they all have the exact same probability distribution.

Question 3

Collection of random variables is i.i.d if?

Answer 3

They are both independent and identically distributed.

Question 4

Samples taken from a finite population without replacement are not?

Answer 4

i.i.d random variables.

Question 5

If the sample size is small, computations can be done by?

Answer 5

Treating them as if they were i.i.d random variables. The difference in computed values will be small.

Question 6

Samples taken from a finite population with replacement are?

Answer 6

i.i.d random variables

Question 7

The procedures in the following sections assume that the sample taken comes from?

Answer 7

i.i.d random variables.

Question 8

!!!Steps of sampling to make estimate of population?

Question 9

Frequency of an interval?

Answer 9

The number of times an outcome (dataset) falls inside the interval (a, b] in n trials. PROBABILITY

Question 10

Frequency distribution of a dataset?

Answer 10

A table that contains two lists: classes of numerical data and the frequency of each class. The classes are disjoint intervals that cover the entire range of a dataset.

Question 11

Frequency histogram and axis? 2•

Answer 11

A graph consisting of bars drawn adjacent to each other.

•Horizontal scale represents classes(bins) of numerical data values

•vertical scale represents frequencies.

Question 12

!!!Classes (bins)?

Answer 12

Numerical data values, independent variable.

Question 13

Relative frequency of an interval (a, b]?

Answer 13

Proportion of times an outcome falls into the interval (a, b] in n trials.

Question 14

Sample density of an interval (a, b]?

Answer 14

Relative frequency of the interval is divided by the length of the interval (a, b]. A sample density is computed so that the area of each bar represents the proportion of data within the corresponding interval.

Question 15

Density histogram? 4•

Answer 15

•x axis: classes(bins)

•y axis: densities

•Heights of bars: sample density values

•area of bar: probability

Question 16

If you don’t know the probability density function, how do you find the probability of an event?

Answer 16

You have to estimate the probability of the event

Question 17

If we get subsections of a probability distribution into several rectangles that estimate the probability from a probability density function and decrease the width of the rectangles as it gets smaller and smaller, then it looks like?

Answer 17

A histogram of each rectangle.

Question 18

As you increase the sample size and plot the histogram of the estimates of a distribution, then?

Answer 18

The histogram starts looking more like the distribution

Question 19

What happens if you make the bins in a histogram too small?

Answer 19

You hide the distribution as it looks more uniform.

Question 20

What happens if you make the bins too big?

Answer 20

Then you will hide the distribution

Question 21

Will a Q-Q plot give you a picture that looks like a density curve?

Answer 21

No

Question 22

Q-Q plot stands for?

Answer 22

Quantile-Quantile plot

Question 23

We don’t know the actual distribution but what still exists?

Answer 23

The guess for quantile of population, Q_p, 0<p<1, and the estimate of quantile (Q^_p), estimator for Q_p

Question 24

A good quantile guess is when?

Answer 24

Q^_p is close to the actual value, Q_p

Question 25

Quantile-quantile plot?

Answer 25

Graph that plots the estimated quantiles of a population (based on a given sample size n) against the corresponding theoretical quantiles of a given population or the estimated quantiles of a second population (based on a given sample size of m).

Question 26

One big assumption of I.I.D?

Answer 26

Each sample must be independent, so you must have replacement in any sample size or you can have no replacement in small sample size.