(iii) A random variable has a triangular probability density function with a = 50, b = 375, and m = 250. (a) Sketch the probability distribution function for this random variable. Label the points a = 50, b (i) = f(x) 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (ii) 0.008 f(x) 0.007- 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X 375, and m = 250 on the x-axis. Choose the correct graph below. (iii) 0.008 f(x) 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X (iv) 0.008 0.007 Graph (i) f(x) 0.006 0.005 0.004 0.003 0.002 0.001 0 0 50 100 150 200 250 300 350 400 X

(Probability) The probability that a phone call will last less than t minutes can be pproximated by the exponential probability function: Probability that a call lasts less than t minutes=1et/a aistheaveragecalllength.eisEulersnumber( 2.71828). For example, assuming the average call length is 2 minutes, the probability that a call will last less than 1 minute is calculated as 1e1/2=0.3297. Using this probability equation, write a C++ program that calculates and displays a list of probabilities of a call lasting less than 1 minute to less than 10 minutes, in 1-minute increments.

(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft