An experiment was conducted to estimate 1/, the 75th percentile (0.75} of the lifetime distribu- tion of a new type of integrated circuit. The 75th...

please answer question one and two with specific steps.

1. An experiment was conducted to estimate 1/, the 75th percentile (0.75} of the lifetime distribu-tion of a new type of integrated circuit. The 75th percentile is the value 7 such that P(X s v} = 0.75. Ten independent selected circuits were tested and the observed lifetimes were: 163.40.21.16. 26.10.41.219. Assuming that the lifetimes follow an exponential distribution with mean 9, find the maximumlikelihood estimate of ”y, where 7 satisfies, .75 = f; f(:c; male = Jéexm—m/fi) d3. 2. Pea plants are classified according to the shape, round (R) or angular (A), and colour, green(G) or yellow (Y), of the peas they produce. According to genetic theory, the four possibleplant types, RG. RY, AG, AY have probabilities afi, (1(1 — 5), (1 — (1)5, and (1 — cr}(1 — (3}.respectively, with different peas being independent of one another. The following table shows the observed frequencies of the four types in 100 plants examined: Oteerved frequenee -Eelislm Find the MLE‘s of a and g3, and compute the estimated expected frequencies for each possibilityunder the model. You need not show the second derivative conditions.