Probability

Question 1

What is the Sample space of a random experiment?

Answer 1

The set of all possible outcomes of the experiment (not the individual variable)

Question 2

If one performs an experiment one of the ___________ in the sample space occurs

Answer 2

Outcomes

Question 3

In the experiment of tossing a coin, what is the sample space?

Answer 3

{HEADS, TAILS}

Question 4

All probabilities add to __

Answer 4

1

Question 5

How do you calculate the relative frequency of an event happening?

Answer 5

Number of times the event occurs / Number of repetitions of experiment

Question 6

What does the relative frequence of an event settle to over many repetitions?

Answer 6

The probability of the event occuring

Question 7

What is the cardinality of the sample space of rolling two dice?

(For example: rolling a 1 then a 1 will give the result (1, 1))

Answer 7

36

Question 8

If A and B are mutually exclusive events, then

A ∩ B = what?

Answer 8

Empty set

Question 9

If A and B are mutually exclusive events then

P(A ∪ B) =

Answer 9

P(A) + P(B)

Question 10

A∪A’ =

Answer 10

S

Question 11

P(A) + P(A’) =

Answer 11

P(S) = 1

Question 12

What is a finite partition of an event B?

Answer 12

A collection of subsets of B

Question 13

The probabilities of all subsets within a Partition add up to ….

Answer 13

The probability of the event happening

Question 14

If

P(A∩B) = P(A)P(B)

then events A and B are _______

Answer 14

Independent

Question 15

If two events do not physically effect each other then they are ____________

Answer 15

Independent

Question 16

P(A|B) = ?

Answer 16

P(A∩B) / P(B)

Question 17

What does P(A|B) mean?

Answer 17

The probability of A given B

Question 18

If A and B are independent then

P(A∩B) = P(A)P(B)

So what is

P(A|B) equal to?

Answer 18

P(A∩B) / P(B)

=

P(A)P(B) / P(B)

=

P(A)

Question 19

In an experiment repeated N times, what is the probability that an event has outcome Z, k times?

Answer 19

Question 20

μ is used to indicate ______

Answer 20

The mean of a random variable

Question 21

The mean of a random variable x can be calculated using the formula

Answer 21

μx = x1p1 + x2p2 + x3p3 + … + xipi = Σxipi

Question 22

Variance is denoted by the symbol

Answer 22

σ²

Question 23

The variance of a random variable X is defined by which formula?

Answer 23

Question 24

The standard deviation of a random variable is equal to

Answer 24

The square root of the variance