Peter and Robert, twoavid skeet shooters, decide to compete as a team in the Bra

Question

Peter and Robert, twoavid skeet shooters, decide to compete as a team in the BrazosSkeet

Invitational. At thisevent, both teammates aim and shoot at every target. Thedelay D

between a target calland its launch is random and distributed uniformly between 0 and3

seconds.

(a) 0.5 pt –Find the probability distribution function (PDF) ofD.

(b) 0.5 pt –Compute the probability that the target is launched within onesecond of the

target call.

Due to his position onthe field, Peter has a better look at targets. The probabilitythat

Peter hits a targetfirst is 0.5; the probability that Robert hits the target first is0.3; and the

probability that atarget remains untouched is 0.2. In one match, a total of 12targets are

used.

(c) 1.5 pt –Find the expected number of targets hit by the team, and find theexpected

number of targets hitby Peter.

(d) 1.5 pt –Find the expected number of targets hit by Peter, given that theteam gets a

total of 6targets.

(e) 1 pt –Find the expected number of targets hit by Peter, given that Robertgets exactly

8 targets.

Explanation / Answer

-Since D can happen at any time with equal probability, theprobability is (1/3). To check if this is right, you can integrate(1/3)dx over (0,3), and you get 1 as your answer. - To find any probability over any period of time, it is simply thearea under the pdf of that interval, i.e., from (0,1) would be theintegral of (x/3) from 0 to 1, or 1/3. - If there are 12 targets, and the odds of hitting first are.5, .3, and .2, simply multiply each expected value by the numberof targets, such that (.5)x12 = 6, .3(12) =3.6, and .2x(12) =2.4 -When you are given that the targets are hit, you can disregard the"the target was not hit" portion, so the odds that Peter hit it is(5/8) and Robert is (3/8). To solve, multiply the odds by thenumber of targets. - To find (e), set up the equation that (3/8) X = 8 Solve for X, and multiply by 5 to get the number peter hit.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.