3) Calculate the variance of the random variable X whose probability distribution is given in he table 10 11 12 13 14 15 P(X = x) 8 | 8 4) Calculate the standard deviation of the random variable X whose probability distribution is given in part 3)

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**Problem 3: Calculating the Variance**

Calculate the variance of the random variable \( X \) whose probability distribution is given in the table below:

\[
\begin{array}{c|cccccc}
x & 10 & 11 & 12 & 13 & 14 & 15 \\
\hline
P(X = x) & \frac{1}{8} & \frac{2}{8} & \frac{1}{8} & \frac{2}{8} & \frac{1}{8} & \frac{1}{8} \\
\end{array}
\]

**Problem 4: Calculating the Standard Deviation**

Calculate the standard deviation of the random variable \( X \) whose probability distribution is given in part 3.
Transcribed Image Text:**Problem 3: Calculating the Variance** Calculate the variance of the random variable \( X \) whose probability distribution is given in the table below: \[ \begin{array}{c|cccccc} x & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline P(X = x) & \frac{1}{8} & \frac{2}{8} & \frac{1}{8} & \frac{2}{8} & \frac{1}{8} & \frac{1}{8} \\ \end{array} \] **Problem 4: Calculating the Standard Deviation** Calculate the standard deviation of the random variable \( X \) whose probability distribution is given in part 3.
Expert Solution
Step 1

3)

Given data,

x

P(X=x)

10

1/8

11

2/8

12

1/8

13

2/8

14

1/8

15

1/8

 

The formula for the expected value of a discrete random variable is,

E(x)=μ=∑x⋅P(X=x)

The formula for the variance of the discrete random variable is,

σ2=∑[(x−μ)2. P(X=x)]

 

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