Statistical Distributions

Question 1

Define a random variable, how it’s represented and an example:

Answer 1

A variable whose value depends on the outcome of a random event.
Represented using upper case letters such as X or Y.
If a coin is tossed 5 times, the random variable could be the number of times heads was tossed.

Question 2

How are the particular values that a random variable can take written?

Answer 2

Using the equivalent lower case letters to the random variable.
For example x and y.

Question 3

How is the probability that a random variable X takes a particular value x written?

Answer 3

P (X=x)

Question 4

Give the values that the random value can take (x) when a fair dice is rolled:

Answer 4

x= 1,2,3,4,5,6

Question 5

What is the sum of all outcomes of an event equal to (Give a numerical way of saying this:

Answer 5

EP(X=x)=1

Question 6

How is a binomial distribution represented when carrying out a number of trials in an experiment or survey (give notation for letters)?

Answer 6

X - B(n,p).
X= random variable.
B stands for binomial.
n = number of trials.
p = probability of success

Question 7

How is P(failure) represented?

Answer 7

1-p

Question 8

Give binomial distribution formula and say what ‘r’ represents:

Answer 8

P(X=r) = (nCr)X(p^r)X(1-p^(n-r)).

r represents number of ways of selecting successful outcomes.