Week 1 - 4.2 Probability Distribution For A Discrete Random Variable

Question 1

Example: Suppose you simultaneously toss two fair coins. Let X be the number of heads observed. Find the
probability associated with each value of the random variable X

Since there are two coins, and each coin can be either heads or tails, there are four possible outcomes(HH,HT,T H,T T),
each with a probability of 1
4 . Since X is the number of heads observed, x = 0,1,2.

We can identify the probabilities of the simple events associated with each value of X as follows:

Example on module

Answer 1

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Question 2

This is a complete description of all the possible values of the random variable, along with their associated probabilities. We refer to this as a

Answer 2

Probability distribution

Question 3

This probability distribution can be represented in different ways.
Sometimes it is represented in

Answer 3

Graphical form or tabular form

Question 4

A probability distribution of a random variable specifies the values the random variable can assume, along with
the probability of it assuming each of these values.

Answer 4

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Question 5

All probability distributions must satisfy the following two
conditions:

Answer 5

P(x) 0,for all values of X
ÂP(x) = 1,for all values of X

Question 6

Example: What is the probability distribution for the number of yes votes for three voters? (See the first example in
the Chapter Introduction.)
Since each of the 8 outcomes is equally likely, the following table gives the probability of each value of the random
variable.

Table 4.3 on module

Tabular representation of the probability distribution for the random variable in the first example in the
Chapter Introduction

Answer 6

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Question 7

The probability distribution of a discrete random variable is a graph, a table, or a formula that specifies the probability
associated with each possible value that the random variable can assume

Answer 7

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