Using the alternative-parameter method, determine the parameters of the following distributions based on the given assessments. Refer to Step 5.5 if necessary.
a. Find the parameter value β for the exponential distribution given P E (T≤15|β) = 0.50.
b. Find the parameters μ and σ for a normal distribution given P N (Y ≤ 125 | μ; σ) = 0.25 and PN (Y ≤ 125 | μ; σ) = 0.75.
c. Find the Min, Most Likely, and Max for the triangular distribution given
PT (Y ≤ 15 | Min; Most Likely; Max) = 0.15,
PT (Y ≤ 50 | Min; Most Likely; Max) = 0.50, and
PT (Y > 95 | Min; Most Likely; Max) = 0.05.
d. Find the parameter values α1 and α2 for the beta distribution given PB (Q ≤ 0.3 | α1; α2) = 0.05 and PB (Q ≤ 0.5 | α1; α2) = 0.25.