Compute the following:

$($a$)$ Consider the slightly modified Bernoulli distribution which is supported by $\{1,2\}($instead of $\{0,1\})$

and where the probability mass of $\{1\}$ is $(1$ p$)$ and the probability mass of $\{2\}$ is p$.$ Compute the

variance of this distribution.

$($b$)$ The mean of the triangular distribution defined above.

$($c$)$ The standard deviation of the uniform distribution on an interval $[$a$,$ b$],$