the table below shows the probability distribution of a random variable y.\n|y|p(y)|\n|-13|0.22|\n|-12|0.4|\n…

Explanation:

Step1: Calculate the expected value $E(Y)$

$E(Y)=\sum_{i}y_iP(y_i)=(-13)\times0.22+(-12)\times0.4+(-11)\times0.21+(-10)\times0.17=-12.03$

Step2: Calculate the variance $Var(Y)$

$Var(Y)=\sum_{i}(y_i - E(Y))^{2}P(y_i)$ $=((-13)-(-12.03))^{2}\times0.22+((-12)-(-12.03))^{2}\times0.4+((-11)-(-12.03))^{2}\times0.21+((-10)-(-12.03))^{2}\times0.17$ $=(-0.97)^{2}\times0.22+(0.03)^{2}\times0.4+(1.03)^{2}\times0.21+(2.03)^{2}\times0.17$ $=0.9409\times0.22 + 0.0009\times0.4+1.0609\times0.21+4.1209\times0.17$ $=0.2070+0.0004+0.2228+0.7006$ $=1.1308$

Step3: Calculate the standard deviation $\sigma_Y$

$\sigma_Y=\sqrt{Var(Y)}=\sqrt{1.1308}\approx1.06$

Answer:

$1.06$