İSTATİSTİK I - Deneme Sınavı - 7

A random experiment is any process that leads to two or more possible outcomes, without knowing
exactly which outcome will occur. The set of all possible outcomes of a random experiment is called the sample space. Each possible outcome of a random experiment is called an elementary outcome. An event occurs if the random experiment results in one of the basic outcomes of that event. A is the correct answer.

I. The complement of an event A is the set of all basic outcomes in S that do not belong to A. (True)

II. The union of events A and B is the set of all elementary outcomes that belong to both sets. (False, The intersection of events A and B is the set of all elementary outcomes that belong to both sets.)

III. The intersection of events A and B is the set of all elementary outcomes that belong to at least one of the sets A and B. (False, The union of events A and B is the set of all elementary outcomes that belong to at least one of the sets A and B.)

The answer is A.

Sometimes it will be important to consider events that do not occur at the same time. That is the events whose intersection is the null event (empty set). If A and B are any two events then they are said to be mutually exclusive if  A ∩ B = 0. The answer is B.

Each dice has a possible outcome of 6 in total {1,2,3,4,5,6}. If they are thrown at the same time the possible outcome would equal to 6*6 = 36. The answer is D.

When order is not important, the arrangements of r objects from n distinct objects is called a combination. The number of combinations of size r from a collection of n objects is denoted by C(n,r), and it is given by C(n,r)= P(n,r)/r! = n!/r!(n - r)! when 0≤r≤n.

For P R O B A B I L I T Y there are in total 11 letters but B and I is used twice so they should be counted only once.

r=9, n=11 therefore 11!/9!(11-9)! = (10*11)/2! = 55. The answer is B.

The answer is C

I. P(AnB) = P(A⏐B)P(B) this formula is called the multiplication rule. (True)

II.  A and B are statistically independent if and only if P(AnB) = P(A)P(B). (True)

III. For A and B sets independence can also be denoted by P(A⏐B). (False, P(A⏐B) denotes conditional probability for sets A and B.)

The answer is C.

The set of all possible outcomes of a random experiment is called the sample space.

A random experiment is any process that leads to two or more possible outcomes, without knowing exactly which outcome will occur.

For example, when a fair die is rolled we know that one of the six faces will show up but we will not be able to say exactly which face will actually show up. Thus, rolling a fair die is an example of a random experiment. Some further examples of random experiments are:

Customers arriving at a particular store during some time interval.

Airplanes taking off in a given time interval at some airport.

Some particular customer requests in a bank.

If A and B are any two events then they are said to be mutually exclusive. The above equation shows this.

In the classical probability approach to assign a probability to an event, the assumption is that all the outcomes have the same chance of happening. 

The empirical probability uses the relative frequencies to assign the probabilities to the events. The empirical probability is based on experiments. In order to find the probability of a specific event, the experiments are repeated many times and the observed outcomes of the event we are interested in is counted.

Sometimes it may not possible to observe the outcomes of events; therefore, the researcher may assign a probability to an event. In subjective probability approach, the researcher assigns a suitable value as the probability of the event. Therefore, a personal judgement comes in to play to assign the probability. This approach is not favorable method to assign probability, but sometimes if there is no previous knowledge on the subject then the researcher may assign a subjective probability as a starting point. Once enough information about the probability of the event is collected then the researcher may revise this initial subjective probability.