Fundamentals of Probability and Statistics for Engineers

154 Fundamentals of Probability and Statistics for EngineersPROBLEMS5.1 Determine the Probability distribution function (PDF) of Y ˆ 3X 1 if(a) Case 1:80; for x < 3;>:31; for x 6:(b) Case 2:80; for x < 3;>: 31; for x 6:5.2 Temperature C measured in degrees Celsius is related to temperature X in degreesFahrenheit by C ˆ 5(X 32)/9. Determine the probability density function (pdf) ofC if X is random and is distributed uniformly in the interval (86, 95).5.3 The random variable X has a triangular distribution as shown in Figure 5.22.Determine the pdf of Y ˆ 3X ‡ 2.5.4 Determine F Y (y) in terms of F X (x) if Y ˆ X 1/2 , where F X (x) ˆ 0, x < 0.5.5 A random variable Y has a ‘log-normal’ distribution if it is related to X by Y ˆ e X ,where X is normally distributed according tof X …x† ˆ" #1…2† exp …x m† 21=2 2 2 ; 1 < x < 1Determine the pdf of Y for m ˆ 0 and ˆ 1.f X (x)1–11xFigure 5. 22 Distribution of X, for Problem 5.3TLFeBOOK