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A physics eXpctiment ceates tpe &l patticle which decavs according to An exponential distribution With mCAn lifetite o 0.| scolds . Fiud(a) Tle pralahility sing...

Question

A physics eXpctiment ceates tpe &l patticle which decavs according to An exponential distribution With mCAn lifetite o 0.| scolds . Fiud(a) Tle pralahility singlee partick lasts ovtr 0 s( untIs(M The probability the average liletime o A0 ot thest created patticles is kxs than 03 mxolddsIn olG eX[HII instantly crente I(X) of these prticler. What Is tl ptolalility Ah the total Gom 0f Iilo| Itu o (cm paurtickn Is greater than 45 mvond? Think autwlit 'hr Mi'is ICTIuS Of avcrakes.

A physics eXpctiment ceates tpe &l patticle which decavs according to An exponential distribution With mCAn lifetite o 0.| scolds . Fiud (a) Tle pralahility singlee partick lasts ovtr 0 s( untIs (M The probability the average liletime o A0 ot thest created patticles is kxs than 03 mxoldds In olG eX[HII instantly crente I(X) of these prticler. What Is tl ptolalility Ah the total Gom 0f Iilo| Itu o (cm paurtickn Is greater than 45 mvond? Think autwlit 'hr Mi'is ICTIuS Of avcrakes.



Answers

Exponential Probability Between 5: 00 PM and 6: 00 PM, cars arrive at Jiffy Lube at the rate of 9 cars per hour $(0.15$ car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within $t$ minutes of 5: 00 PM. $$ F(t)=1-e^{-0.15 t} $$ (a) Determine how many minutes are needed for the probability to reach $50 \%$. (b) Determine how many minutes are needed for the probability to reach $80 \%$.

Mhm. The probability That the random variable is greater than or equal to two Equals the probability that it equals to plus the probability that it equals three plus the probability that it equals four And this equals .05, 1.05 Plus zero Robot, Their vehicles .1 thought, and the expectation echoes the sun of the value of X I times its probability metric, als zero times 00.7 Plus one times .15 plus two points times 0.5 plus three times 30.5 and plus four times 40.5 Hence their sickles, points 15 last 0.1 Plus .15 plus point to Which vehicles .6.

Yes. Mhm. It is a problem. The setting is the time series but we can set them as define as the minutes. So it's a 30B 10 record that we actually calculate them in minutes. So So actually B -A. is 90 minutes. Yes. And following this setup we can calculate them function. The committee distribution function would be Yeah. So it will be zero F X. Is smaller than a 30. And it's going to be 1/90 X -830. Right? When Ex ranged from 8 30 to 10. Okay. It's also going to be one if access Great. Very good. End 9 30 10 30. So this is a problem. A problem. B We have the expected value would be a plus B over two and it's gonna be 9 10 50 The variance of it should be 90 square or towel and it's going to be 675 Problems. See so we have three time period because daily in here and we got 10 minutes and over the probability should be one of three. For problem there we have three but here we have 10 minutes and it's over 90 then probably to over three. So that would finish the

Mhm. According to the definition, the probability that the random variable X. Is greater than we called you, too, because The probability that equals two plus the probability the articles. Mhm. Which vehicles .05 plus .05 Read trickles .1. Mhm. Mhm. And the expectation he calls the south of exciting times its probability. And so there's Eco's zero times 0.8, last one times, mhm 0.1 plus two times .05 Plus three times .05. And this tickles .35 Yeah, participation.


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