A string has a length of 5 units. A point is chosen on the string randomly and t

Question

A string has a length of 5 units. A point is chosen on the string randomly and the string is cut at a length X (to that point), what is the probability that this segment is at least 1.5 times longer than the remaining piece? The lifetimes of computers is modeled in terms of a Rayleigh density. Three manufacturers A, B, C are available. Their computers have average lifetimes of 5, 6 and 7 years respectively. A company orders 20 computers from A, 30 from B and 50 from C. What is the probability that a computer randomly examined is operating beyond 6 years? 3. 4.

Explanation / Answer

length of the string = 5

value of X at which it is 1.5 times longer than the remaining piece be k

so k+k/1.5 = 5 => 2.5k = 5*1.5

k = 3

so X need to be greater the 3 to satisfy the codition that X should be atleast 1.5 greater than the remaining string

probabilty of X>x in uniform distribution is (b-x)/(b-a) where X is uniformly distributed between and

so P(X>=3) = (5-3)/(5-0) = 2/5 = 0.4

probability that this segemnt is at least 1.5 times longer than the remaining piece = 0.4

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