Question

The following table shows the probability distribution for a discrete random variable. X 12 15 17 20 22 24 25 30 P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08 What is the mean of this discrete random variable? (That is, what is E(X), the expected value of X?) A. 20 B. 19.59 C. 20.625 D. 21

Answer 1

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.

$\large {\boxed {E(x) = \mu = \sum x_ip_i} }$

$\texttt{ }$

Given: The probability distribution for a discrete random variable:

$\boxed{\texttt{ X\ \ }}\boxed{\texttt{ 12\ \ \ }}\boxed{\texttt{ 15\ \ \ }}\boxed{\texttt{ 17\ \ \ }}\boxed{\texttt{ 20\ \ \ }}\boxed{\texttt{ 22\ \ \ }}\boxed{\texttt{ 24\ \ \ }}\boxed{\texttt{ 25\ \ \ }}\boxed{\texttt{ 30\ \ \ }}$

$\boxed{\texttt{P(X)}}\boxed{\texttt{ 0.07 }}\boxed{\texttt{ 0.21 }}\boxed{\texttt{ 0.17 }}\boxed{\texttt{ 0.25 }}\boxed{\texttt{ 0.05 }}\boxed{\texttt{ 0.04 }}\boxed{\texttt{ 0.13 }}\boxed{\texttt{ 0.08 }}$

From the above table, the mean can be calculated:

$E(x) = \mu = 12 ( 0.07 ) + 15( 0.21 ) + 17(0.17) + 20( 0.25 ) + 22(0.05) + 24(0.04) + 25(0.13) + 30(0.08)$

$E(x) = \mu = 0.84 + 3.15 + 2.89 + 5 + 1.1 + 0.96 + 3.25 + 2.4$

$E(x) = \mu = 19.59$

Conclusion:

The mean of this discrete random variable is 19.59

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

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

Answer 2

The mean of this discrete random variable can be calculated by finding for the summation of the weighted average:

Mean = Summation (Xi * P(Xi))

Therefore,

Mean = 12 (0.07) + 15 (0.21) + 17 (0.17) + 20 (0.25) + 22 (0.05) + 24 (0.04) + 25 (0.13) + 30 (0.08)

Mean = 19.59

Therefore the answer is letter B. 19.59