Question

Find the variance of this probability distribution. Round to two decimal places.​

Answer 1

Variance = 4.68

Explanation:

The formula for the variance is:

`\sigma^(2) =(\Sigma(X- \mu)^(2))/(N) \\or \\ \sigma^(2) =(\Sigma(X)^(2))/(N) -\mu^(2) \\`

Where:

`X: Values \\\mu: Mean \\N: Number\ of\ values`

The mean can be calculated as each value multiplied by its probability

`\mu = 0*0.4 + 1*0.3 + 2*0.1+3*0.15+ 4*0.05=1.15`

`(\Sigma (X)^(2))/(N) =((0^(2)+1^(2)+2^(2)+3^(2)+4^(2)))/(5) =6`

Replacing the mean and the summatory of X:

`\sigma^(2) = (\Sigma(X)^(2))/(N) -\mu^(2) \\= 6 - 1.15^(2)\\= 4.6775`