Suppose the reaction temperature ?X ?(in ?C) in a certain chemical process has a uniform distribution with A = -5 and B = 5. a.? ?Compute P(X <0). b.? ompute P(-2.5 < X <2.5). c.? ?ComputeP(-2 ? X ? 3). d. For k satisfying -5 < k < k + 4 <5, compute P(k < X < k + 4).

Solution: Step 1 : It is given that the reaction temperature X in a certain chemical process have a uniform distribution. With A=-5 anb B=5. we have to find the probabilities for different ranges of X. Here X~ U(A,B). So the probability density function of uniform distribution 1 f(X)= BA , A X B Step 2 : a) we have to find P(X <0) In this case the probability mass function will be 1 f(X)= 10 , -5 X 5 So 0 P(X <0) = 5 1/10 dx 0 = 1/10 [x]5 =½ Similarly 2.5 b) P(-2.5 < X <2.5) =2.51/10 dx = ½ 3 c) P(-2 X 3) = 1/10 dx 2 =½