Question

Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. X: 0 1 2 3P(x): 0.085 0.336 0.421 0.158

Answer 1

xpThe data is given as

X: 0 1 2 3

P(x): 0.085 0.336 0.421 0.158

To find the standard deviation , first find the mean of the variable.

The mean is calculated as

`\mu=\Sigma xP(x)=0+0.336+0.842+0.474=1.652`

Now another table,

Now the formula for standard deviation is determined as

`\sigma=\sqrt[]{\Sigma(x^2P(x))-\mu^2}`
`\sigma=\sqrt[]{3.442-1.652^2}=\sqrt[]{3.442-2.729104}=\sqrt[]{0.712896}`
`\sigma=0.8443`

Thus the standard deviation is 0.8443.