Using the alternative$-$parameter method, determine the parameters of the following distributions based on the given assessments.

a$.$ Find the parameter value for the exponential distribution given PE$($T a$.<=15|$ $)=0\mathrm{.}50.$

b$.$ Find the parameters and $$ for a normal distribution given PN$($Y $<=25|$ $,)=0\mathrm{.}25$ and PN$($Y $<=125|$ $,)=0\mathrm{.}75.$

c$.$ Find the Min, Most Likely, and Max for the triangular distribution g$1$ven

Pr$($Y $<=15|$Min$,$ MostLikely, Max$)=0\mathrm{.}15,$

Pr$($Y $<=50|$Min$,$ MostLikely, Max$)=0\mathrm{.}50$ and

Pr$($Y $>95|$Min$,$ MostLikely, Max$)=0\mathrm{.}05.$

d$.$ Find the parameter values $1$ and $2$ for the beta distribution given PB$($Q $<=0\mathrm{.}3|$ $1,$ $2)=0\mathrm{.}05$ and PB$($Q $<=0\mathrm{.}5|$ $1,$ $2)=0\mathrm{.}25$