Question

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

Answer 1

Answer:

Variance = 4.68

Step-by-step explanation:

The formula for the variance is:

$\sigma^{2} =\frac{\Sigma(X- \mu)^{2}}{N} \\or \\ \sigma^{2} =\frac{\Sigma(X)^{2}}{N} -\mu^{2}$

Where:

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

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

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

$\frac{\Sigma (X)^{2}}{N} =\frac{(0^{2}+1^{2}+2^{2}+3^{2}+4^{2})}{5} =6$

Replacing the mean and the summatory of X:

$\sigma^{2} = \frac{\Sigma(X)^{2}}{N} -\mu^{2} \\= 6 - 1.15^{2}\\= 4.6775$