Defination of a Random Variable, concept of a Random Variable, types of random variable and assignment

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What you will learn??
1. Definition of a Random Variable.
2. Concept of a Random Variable
3. Types of Random variable
4. Assignment.

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• Defination: Random variable is a single real valued function from a
sample space S into the real numbers.
• Generally, It is denoted by capital letters like A,B,C,…,X,Y,Z.
• let us define a random variable “Number of heads in the following tosses
of a coin”

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• Example: In tossing a fair coin, the possible outcomes are “head” and
“tail” resp. i.e.
S = {H,T}
Again if we toss a coin two times then the
possible outcomes are
S = {HH,HT,TH,TT}
Now, if we toss a coin a three times,
S = {HHH,HHT,HTT,TTT,THH,TTH,HTH,THT}
• space of a random variable is {0,1,2,3}
Concept of a Random Variable
s HHH HHT HTT TTT THH TTH HTH THT
X(s) 3 2 1 0 2 1 2 1

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Generalization
Now, we might decide to toss a coin 50 times and note that sample
space contains 2^50 elements, each containing a order strings of “H”
and “T” of length 50.
Sample space increases and it becomes very difficult to calculate the
desired probability.
We should be able to reduce this to a reasonable size! It may be that
the only quantity of interest is the number of heads in 50 tosses of a
coin.
Note, that the sample space of a random variable is the set of
integers {0,1,…,50}

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• Random variable is of two types:
1. Discrete Random variable: A variable which can take only a countable
number of real values.
example: 1. number of deaths
2. number of accidents
1. Continuous Random variable: A random variable X is said to be
continuous if it can take all possible values i.e. integral as well as
fractional between certain limits.
example: 1. heights of an individuals
2. temperature of a city.
Types of Random variable

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• Suppose, we toss a coin 4 times.
• What is the sample space of this experiment??
• What is the space of Random variable X ??
Where X is defined as “number of tails in 4 tosses of coin”
• What is the probability of getting atleast one head ??
Submit it on www.stepupanalytics.com for evaluation
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Assignment