Question

7. The variable Home Ownership can take on one of two values: 1 if the person living in the home owns the home and 0 if the person living in the home does not own the home. This is an example of a __________variable.

8) Using the following probability distribution table of the random variable x, what is the probability of x = 3?

X	P(X)
0	5/15
1	4/15
2	1/15
3

9) The binomial distribution is characterized by situations that are analogous to

A) drawing balls from an urn.

B) coin tossing.

C) counting defects on an item.

D) measuring the length of an item.

Answer 1

Solution:

Question: The variable Home Ownership can take on one of two values:

1 if the person living in the home owns the home and

0 if the person living in the home does not own the home.

This is an example of a Bernoulli variable.

Since Bernoulli can have only two possible outcomes either success or failure.

Question 8)

Given:

X	P(X)
0	5/15
1	4/15
2	1/15
3	---

We have to find: P( X = 3) =........?

Since total probability is 1, we use following steps:

P(X=0)+P(X=1)+P(X=2)+P(X=3)= 1

5/15 + 4/15 + 1/15 + P(X=3)= 1

(5+4+1) / 15 + P(X=3)= 1

10/15 +P(X=3)= 1

P(X=3)= 1 - 10/15

P(X=3)= (15-10)/15

P(X=3)= 5/15

Question 9) The binomial distribution is characterized by situations that are analogous to____.

In binomial distribution, we assume each trial has only two possible outcomes, that is Bernoulli trials.

Thus if an experiment can results in only two possible outcomes, that is Bernoulli trials,then such a experiment follows Binomial distribution.

A) drawing balls from an urn can be more than 2, so this is not binomial distribution.

B) coin tossing. In coin tossing we can have Head or Tail, that is only two possible outcomes, that is Bernoulli trials.

The binomial distribution is characterized by situations that are analogous to coin tossing.

C) counting defects on an item. It can be like 0,1,2,3,........, So outcomes can take any number of values.

Thus this is not binomial distribution situation.

D) measuring the length of an item. Length of an item can not be considered as success or failure, thus this is not binomial distribution situation.

Thus correct answer is B) Coin tossing.