b. What is the probability that work has a density higher than .7? c. Consider a

Question

b. What is the probability that work has a density higher than .7? c. Consider a social network with only 2 members. Explain why the uniform model would not be a good approximation for the distribution of network density. Timber beams are widely used in home construction. When the load (measured in pounds) per unit length has a constant value over part of a beam, the load is said to be uniformly distributed over that part of the beam. Uniformly distributed beam loads were used to derive the stiffness distribution of the beam in the American Institute of Aeronautics and Astronautics Journal (May 2013). Consider a cantilever beam with a uniformly distributed load between 100 and 115 pounds per linear foot. a. What is the probability that a beam load exceeds 110 pounds per linear foot? b. What is the probability that a beam load is less than 102 pounds per linear foot? c. Find a value L such that the probability that the beam load exceeds L is only .1.

Explanation / Answer

5.15 (a) Here X = is the beam load per linear foot

so fX(x) = 1/(115 -100) = 1/15 where 100 <= X <= 115

and CDF F(x) = (x-100)/15

Here we have to calculate the probability of x>= 110

Pr( X>=110) = 1 - Pr(X<110) = 1 - (110-110)/15 = 1/3 = 66.67%

(b) Here we have to calculate Pr( X<= 102) = (x-100)/15 = (102 -100)/15 = 2/15 = 0.133

(c) Here Pr(X>=L) = 0.1

P(X<L) = 0.9

so F(x) = 0.9 = (x -100)/15

x = 100 + 0.9 * 15 =113.5 load per linear foot

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