Question

The data from 225 endothermic reactions involving sodium bicarbonate are summarized as follows: Number of Reactions Final Temperature Conditions 264 K 282 K 294 K 50 79 96 A) Calculate the probability mass function of final temperature. B) Determine the cumulative distribution function for the random variable.

Answer 1

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A let X= final Tempena ture. na total no. of reactions = 225 50 = 0.22222 225 P ( X = 264K) = P ( X =2124) = 2 P = 0.3511 79 225

96 P(x=2946) = 0.42666.7 225 f Probability mass tion of final funct temperature X is (1) = 1.22222 jefx=2648. if x=2826 o 35 lll 2 0.426667 if a=294k > B let Flu) be C.D.F of x . x < 264 K. =0.22222 e 264 2u2282 > F(x)=0 four F(a)= (^2 F(x)= |(204) +Þ(282) = 0.57333 F(M)-1 if 2822 x 2294 2 294 S x. 7 Thus, C.D.f final of temperature is if x<264k f(x) 0.22222 2 264 L x<282k if 0.57333 2 if 282K3 X<294K x 71 294k 1 if