Question

In: Statistics and Probability

List the characteristics of a multinomial experiment (select all that apply): a) The probability that the...

List the characteristics of a multinomial experiment (select all that apply):

a) The probability that the outcome of a single trial falls into a particular category remains constant from trial to trial.

b) The trials are independent.

c) The experiment consists of n identical trials.

d) The outcome of each trial falls into one of k categories.

e) Each trial results in one of only two possible outcomes.

f) The experiment contains M successes and N − M failures.

g) The probability that the outcome of a single trial falls between two categories is equal to the area under the curve between those categories.

h) The experimenter counts the observed number of outcomes in each category.

i) The number of successes is evenly distributed over all k categories.

j) Its mean is 0 and its standard deviation is 1.

k) We are interested in x, the number of events that occur in a period of time or space.

l) We are interested in x, the number of successes observed during the n trials.

Solutions

Expert Solution

The correct statements are:

a) The probability that the outcome of a single trial falls into a particular category remains constant from trial to trial.

b) The trials are independent.

c) The experiment consists of n identical trials.

d) The outcome of each trial falls into one of k categories.

g) The probability that the outcome of a single trial falls between two categories is equal to the area under the curve between those categories.

h) The experimenter counts the observed number of outcomes in each category.

k) We are interested in x, the number of events that occur in a period of time or space.

The false statements are:

e) Each trial results in one of only two possible outcomes.

Reason: There are actually K categories i.e. set of outcomes

f) The experiment contains M successes and N − M failures.

Reason: This is actually the characteristic of Bernoulli trials

i) The number of successes is evenly distributed over all k categories.

Reason: Probability cannot be generalized as equally likely

j) Its mean is 0 and its standard deviation is 1.

Reason: Mean and standard deviation cannot be generalized for the experiment

l) We are interested in x, the number of successes observed during the n trials.

Reason: This is actually the characteristic of Bernoulli trials

orchestra answered 1 year ago

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