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Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has the given pdr. (( x ) = = (4 - * 2 ) -1s x$ 2 otherwise (a) Sketch the graph of /(x). [(x) [(x) [(x) [(x) 0.5 0.3 0.25 0.20 0.4 0.20 0.15 0.2 0.3 0.15 0.10 0.1 0.2 0.10 0.05 0.05 0.1 0.00 DO 0.00 0.0 O -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 1.0 -0.5 0 0.5 1.0 1.5 2.0 1.0 -0.5 0 0.5 1.0 1.5 2.0 O -1.0 -0.5 0 0.5 1.0 2.0 (b) Determine the cdf. x 2 Sketch the cdf. F(x) F(x) F(X) F(x) 1.0 1.0 1.0 1.0 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.0 0.0 0.0 0.0 -1 2 2 2 2 ) Is 0 the median temperature at which the reaction takes place? If not, is the median temperature smaller or larger than 0? The median temperature is 0 if and only if F(0) = 0.5. Since F(0) -Select - V equal 0.5, this -Select- the case. Since A(0) [? V 0.5, the median must be | Select- v ] 0. (d) Suppose this reaction is independently carried out once in each of ten different labs and that the pdf of reaction time in each lab is as given. Let Y = the number among the ten labs at which the temperature exceeds 1. What kind of distribution does Y have? (Give the names and values of any parameters.) O Y is an exponential distribution with parameter 1 = = Y is an exponential distribution with parameter 1 = - O Y is a binomial distribution with parameters n = 10 and p = - O Y is a binomial distribution with parameters n = 10 and p = =