Question

the table below shows the probability distribution of a random variable y:
y p(y)
8 0.2
9 0.6
10 0.2
what is the standard deviation of y?
round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the expected value E(Y)

$E(Y)=\sum_{i}y_ip_i = 8\times0.2 + 9\times0.6+10\times0.2=1.6 + 5.4+2=9$

Step2: Calculate the variance Var(Y)

$Var(Y)=\sum_{i}(y_i - E(Y))^2p_i=(8 - 9)^2\times0.2+(9 - 9)^2\times0.6+(10 - 9)^2\times0.2=(- 1)^2\times0.2+0^2\times0.6+1^2\times0.2=0.2 + 0+0.2 = 0.4$

Step3: Calculate the standard deviation SD(Y)

$SD(Y)=\sqrt{Var(Y)}=\sqrt{0.4}\approx0.63$

Answer:

$0.63$