Random Variables Notes | EduRev

: Random Variables Notes | EduRev

 Page 1


Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Page 2


Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
random variable:
• # on green die
• sum of roll (green die + red die)
• product of roll
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Page 3


Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
random variable:
• # on green die
• sum of roll (green die + red die)
• product of roll
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
not not a random variable:
• color of die with highest number
• score on each die (green die, red die)
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Page 4


Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
random variable:
• # on green die
• sum of roll (green die + red die)
• product of roll
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
not not a random variable:
• color of die with highest number
• score on each die (green die, red die)
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Flip a coin…
S = {head, tails}
Random Variables
Random Variables
In general, we can obtain a random variable by simply
assigning a numerical value assigning a numerical value to each outcome of a given
experiment. 
How can we create a random variable from this experiment?
Page 5


Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
random variable:
• # on green die
• sum of roll (green die + red die)
• product of roll
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Example Example: roll two dice
not not a random variable:
• color of die with highest number
• score on each die (green die, red die)
Random Variables
Random Variables
A random variable is a real-valued function with a domain in
the sample space S.
f f : S ? R
Flip a coin…
S = {head, tails}
Random Variables
Random Variables
In general, we can obtain a random variable by simply
assigning a numerical value assigning a numerical value to each outcome of a given
experiment. 
How can we create a random variable from this experiment?
Flip a coin…
S = {head, tails}  ? {0,1}
Random Variables
Random Variables
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