Answer:
Variance = 4.68
Step-by-step explanation:
The formula for the variance is:
[tex]\sigma^{2} =\frac{\Sigma(X- \mu)^{2}}{N} \\or \\ \sigma^{2} =\frac{\Sigma(X)^{2}}{N} -\mu^{2} \\[/tex]
Where:
[tex]X: Values \\\mu: Mean \\N: Number\ of\ values[/tex]
The mean can be calculated as each value multiplied by its probability
[tex]\mu = 0*0.4 + 1*0.3 + 2*0.1+3*0.15+ 4*0.05=1.15[/tex]
[tex]\frac{\Sigma (X)^{2}}{N} =\frac{(0^{2}+1^{2}+2^{2}+3^{2}+4^{2})}{5} =6[/tex]
Replacing the mean and the summatory of X:
[tex]\sigma^{2} = \frac{\Sigma(X)^{2}}{N} -\mu^{2} \\= 6 - 1.15^{2}\\= 4.6775[/tex]
