The mean of this discrete random variable is B. 19.59
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
Let us tackle the problem !
The mean of discrete random variable could be calculated by using this following formula.
[tex]\large {\boxed {E(x) = \mu = \sum x_ip_i} }[/tex]
[tex]\texttt{ }[/tex]
Given: The probability distribution for a discrete random variable:
[tex]\boxed{\texttt{ X\ \ }}\boxed{\texttt{ 12\ \ \ }}\boxed{\texttt{ 15\ \ \ }}\boxed{\texttt{ 17\ \ \ }}\boxed{\texttt{ 20\ \ \ }}\boxed{\texttt{ 22\ \ \ }}\boxed{\texttt{ 24\ \ \ }}\boxed{\texttt{ 25\ \ \ }}\boxed{\texttt{ 30\ \ \ }}[/tex]
[tex]\boxed{\texttt{P(X)}}\boxed{\texttt{ 0.07 }}\boxed{\texttt{ 0.21 }}\boxed{\texttt{ 0.17 }}\boxed{\texttt{ 0.25 }}\boxed{\texttt{ 0.05 }}\boxed{\texttt{ 0.04 }}\boxed{\texttt{ 0.13 }}\boxed{\texttt{ 0.08 }}[/tex]
From the above table, the mean can be calculated:
[tex]E(x) = \mu = 12 ( 0.07 ) + 15( 0.21 ) + 17(0.17) + 20( 0.25 ) + 22(0.05) + 24(0.04) + 25(0.13) + 30(0.08)[/tex]
[tex]E(x) = \mu = 0.84 + 3.15 + 2.89 + 5 + 1.1 + 0.96 + 3.25 + 2.4[/tex]
[tex]E(x) = \mu = 19.59[/tex]
Conclusion:
The mean of this discrete random variable is 19.59
Learn more
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation , DIscrete , Random , Variable , Expected , Value , E(x) , Table
