Compute the Variance and Standard Deviation of a Discrete Random Variable
-The owner of a farmer s market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline P(x) & 0.05 & 0.19 & 0.20 & 0.25 & 0.12 & 0.10 & 0 & 0.08 & 0 & 0.01 \
\hline
\end{array}$

A) $3.57$
B) $1.95$
C) $3.97$
D) $0.56$

Question

Compute the Variance and Standard Deviation of a Discrete Random Variable
-The owner of a farmer s market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline P(x) & 0.05 & 0.19 & 0.20 & 0.25 & 0.12 & 0.10 & 0 & 0.08 & 0 & 0.01 \
\hline
\end{array}$

A) $3.57$
B) $1.95$
C) $3.97$
D) $0.56$

Quizplus · Accepted Answer

The variance is calculated using the formula $\sigma^2 = \sum (x_i - \mu)^2 P(x_i)$, where $\mu$ is the expected value. First, calculate $\mu = \sum x_i P(x_i) = 3.57$. Then, compute the variance using the probabilities and the mean. The result is approximately 3.57.