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The probability that a three-person jury will make a correct decision is given by the function below, where 0<α<1 is the probability the person is guilty of the crime, r is the probability that a given jury member will vote "guilty" when the defendant is indeed guilty of the crime, and s is the probability that a given jury member will vote "innocent" when the defendent is indeed innocent. Complete parts a through c. P(α,r,s)=α[3r2(1−r)+r3]+(1−α)[3s2(1−s)+s3] a. Calculate P(0.9,0.5,0.8) and P(0.1,0.7,0.2) and interpret your answers. P(0.9,0.5,0.8)= (Do not round until the final answer. Then round to three decimal places as needed.)
a. To fit the data to a function of the form y=abt, where t is the number of years since 1985 and y is the number of transistors (in millions), take the natural logarithm of both sides of the equation to get lny=lna+tlnb. Then let w=lny,r=lna, and s=lnb to form w=r+st. Using linear regression, find values for r and s that will fit the data above. w=()+1)t (Round to four decimal places as needed.)
The process of frying food changes its quality, texture, and color. Suppose the total change in color E (which is measured in the form of energy as kJ/mol ) of blanched potato strips can be estimated by the function below, where C is the temperature (in ∘C ) and t is the frying time (in min). Complete parts a through c. E(t,C)=433.58−10.42t−5.51C−0.02t2+0.02C2+0.08Ct a. What is the value of E prior to cooking? (Assume that C=0.) E=kJ/mol (Type an integer or a decimal.)
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