Fundamentals of Probability and Statistics for Engineers

68 Fundamentals of Probability and Statistics for Engineersp X(x)f X (x)0.640.2(a)1 2 3x(b)xFigure 3. 19 The probability mass function, p X (x), and probability density function,f X (x), for Problem 3.33.3 For p X (x) and f X (x) in Figure 3.19(a) and 3.19(b) respectively, sketch roughly inscale the corresponding PDF F X (x) and show on all graphs the procedure forfinding P(2 < X < 4).3.4 For each part, find the corresponding PDF for random variable X.(a) Case 1:0:1; for 90 x < 100;f X …x† ˆ0; elsewhere:(b) Case 2:f X …x† ˆ2…1 x†; for 0 x < 1;0; elsewhere:(c) Case 3:f X …x† ˆ3.5 The pdf of X is shown in Figure 3.20.(a) Determine the value of a.(b) Graph F X (x) approximately.(c) Determine P(X 2).(d) Determine P(X 2jX 1).1…1 ‡ x 2 ;†for 1 < x < 1:3.6 The life X, in hours, of a certain kind of electronic component has a pdf given by8< 0; for x < 100;f X …x† ˆ: 100;x2 for x 100:Determine the probability that a component will survive 150 hours of operation.TLFeBOOK