Question: Find the expected value, variance, and standard deviation of \(X\) in the following probability distributions:

a \(\mathrm{P}(X=1)=0.05, \mathrm{P}(X=2)=0.45, \mathrm{P}(X=3)=0.30, \mathrm{P}(X=4)=0.20\)

b \(\mathrm{P}(X=-20)=0.13, \mathrm{P}(X=0)=0.58, \mathrm{P}(X=100)=0.29\).

c \(\mathrm{P}(X=0)=0.368, \mathrm{P}(X=1)=0.632\).

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