xpThe data is given as
X: 0 1 2 3
P(x): 0.085 0.336 0.421 0.158
To find the standard deviation , first find the mean of the variable.
The mean is calculated as

Now another table,
Now the formula for standard deviation is determined as
![\sigma=\sqrt[]{\Sigma(x^2P(x))-\mu^2}](https://img.qammunity.org/2023/formulas/mathematics/college/lgwgdrm5e9pr94pvdtxzwzaj1ogz27ziwq.png)
![\sigma=\sqrt[]{3.442-1.652^2}=\sqrt[]{3.442-2.729104}=\sqrt[]{0.712896}](https://img.qammunity.org/2023/formulas/mathematics/college/d5o0rqxxkyuqmfv0nt8fn2rau9rcojfk3w.png)

Thus the standard deviation is 0.8443.