4

6 points) Experiments by Rutherford and Geiger in 1910 showed that the number of alpha particles emitted per unit time in a radioactive process is a random variable...

Question

6 points) Experiments by Rutherford and Geiger in 1910 showed that the number of alpha particles emitted per unit time in a radioactive process is a random variable having Poisson distribution_ Let X denote the count over one second and suppose it has mean 5_ 2 points) What is the probability of observing fewer than two particles during any given second? 4 points) Lct Y dcnotc thc count Ovcr & scparatc pcriod of 1.5 seconds. What is P(Y > 10)?

6 points) Experiments by Rutherford and Geiger in 1910 showed that the number of alpha particles emitted per unit time in a radioactive process is a random variable having Poisson distribution_ Let X denote the count over one second and suppose it has mean 5_ 2 points) What is the probability of observing fewer than two particles during any given second? 4 points) Lct Y dcnotc thc count Ovcr & scparatc pcriod of 1.5 seconds. What is P(Y > 10)?



Answers

In the 1910 article "The Probability Variations in the Distribution of $\alpha$ Particles" (Philosophical Magazine, Series 6, No. 20, pp. 698-707), E. Rutherford and H. Geiger described the results of experiments with polonium. The experiments indicate that the number of $\alpha$ (alpha) particles that reach a small screen during an 8 -minute interval has a Poisson distribution with parameter $\lambda=3.87 .$ Determine the probability that, during an 8 -minute interval, the number, $Y,$ of $\alpha$ particles that reach the screen is a. exactly four. b. at most one. c. between two and five, inclusive. d. Construct a table of probabilities for the random variable $Y$. Compute the probabilities until they are zero to three decimal places. e. Draw a histogram of the probabilities in part (d). f. On average, how many alpha particles reach the screen during an 8-minute interval?

Hello everyone. This is problem 85. Mhm. Why is equal to the number of alpha particles reaching a screen? Oh no. Why is distributed as a post song With λ equal to 3.87 which is our mean and little one can take on values 01 and so on. The probability that capital Y. Is equal to little Y. Is equal to land to the Y. E. To the negative lander over wife victoria. For part A. We want to know what is the probability But why is equal to 4? Which is equal to 3.87 to the 4th E. to the negative 3.87 over four factorial. We will use Excel to figure it out now. For part B. We have the probability that why is listener you could one meaning why could only take on the values you're on one? So it's equal to Probability of why is equal to zero plus the probability The Y. is equal to one. And for part C We want to find the probability that why takes on values between two and five inclusive, meaning that um It could take on values uh 234 and five. The Y. Okay. Uh Now for party and IV uh part D we just need to figure out some probabilities and party draw a instagram. Okay, so if you want to do this in excel, you need to use this part right here. So you just write down the equal sign because that's how functions are taking in Excel. And you type person the Dist So we know we're talking about the person distribution. Ah the zero there is because I'm trying to find The probability that Y is equal to zero and the 3.87. That's your land right here. Which is a mean. And you also need to put false because we're not talking about the community distribution. Okay? No, if we just look at part A we're trying to find the probability that was the group for which is going to be right here. .195 to three decimal places. So let's write that down 0.195. For part b. Notice that we need to probably a Hawaii 0-0 for the problem Y is equal to one. So if we add up These two numbers right here, your point to one and .081, um we'll get point 102 there and then for the problems that two is a very good y which is a very good fine. Which is sick. We need to add up the probability that why is equal to two, 3, 4 and five. So plus four numbers, if you add that on your calculator you'll get 0.704. Now for party they wanted this is party right here. Ah They wanted the probabilities of 20 with uh three decimal places. So that means that um they're supposed to be three zeros after the decimal point. So that is it for the for part e uh we need to draw hissed a gram of this part right here. And so we did um I used Excel as well and said this part right? Support A to be the X axis and then be yeah to be the lack axis. And I just put that it was a bar graph because it only takes whole numbers for part F. We have that on average 3.87 alpha particles. Mhm. Reach the screen during and eight minutes and True, Okay.

This problem when you use place on distributions and we're told that radioactive radioactive atoms are on its stable because they have too much energy and when they released this extra energy, they're said to decay. So here we're studying cesium 137 and it's found that during the course of decay over a year. So 365 days, there's a million radioactive atoms are reduced to 977,287 radioactive atoms. So for part a we want to find the mean number of radioactive atoms that are lost through decay in monday. And so we know that 22,713 items decade In 365 days. So the mean is the sum of all the values divided by the member of the values. So expire is equal to the sum Michaels went to end. So over in And the number of decades, decade items is the sum of all the values. And the number of values is the number of days since we're interested in the new number of decade atoms in a day. So it's going to be the 22007 and 13. We're 365. Which will give us a means of 62.227 Adams predict. And then in part these we want to find the probability that on a given day 60 radioactive Find the probability that only given day 50 radioactive atoms have decayed. And so we're going to use our formula for probability for a voice on distribution. So it's P. M. X. Is equal to you to act transparently the mule times expect or over X. Factorial. And so here we have the mean number per days, the year total divided by the number of days in a year. So our meal is going to be one million minus the amount looked over at the end of the year. Over 365 like we found in part a um it's this and so now we can replace new with that value and X with 50 So we'll have p 50 is equal to. Mhm. Yeah. Mhm. This is over 50 years. Factorial. This will give us a probability of 0.0155.

Welcome to enumerate in the current problem, lambda is equals 25 And we have to find the probabilities for the values of x equals 012 dot dot dot dot till six. Okay, so we have to find values P0P even piece everything. Now we know the Poggio PMF is it was the power minus lambda into lambda. To the power X divided by X factorial. Which is it's the power minus five into five. To the power X by five. Factory in. Now, if you want to find 40 you have to Put 20 over here and hopes not by factorial. It is X factorial right and over here to places and for that you have to write each and every term on the calculated. So rather than going that way, we will take another approach. But before that we will just find out P zero. That would be to the power minus five into five. To the power zero by zero factorial. Now this and this boat are one and You to keep our -5 Would be 0.00 6738. Okay. Now following the same procedure we can find the one P two P three but I want to be a little faster in the examination hall so I don't want to do all those calculations. What I will do is I would rather have this recovery in relation remembered. Okay because if you see What will be P one, P 1 will be okay instead of lambda. Okay. Um This is lambda only but for us it will be lambda by one in 20 five x 1 into P zero. Same way P two would be five x 2 into P one. P three would be five x 3. The two before would be five by food before and P five would be five by five. Oh I'm sorry P three P three over here. So this would be before correct? And P six would be five by six. P five, correct? No, you might be wondering here also we are taking a lot of steps. How is it reducing our work Now? Think for this P0, you will write in the step five into 0.006738 Now, Was there already on screen? So all you do is answer into five and you got P one. How Much is People? No, 0.03369. Now, imagine for this is this is our P one. So what will you do now with P even with answer you multiply five divide by two. How is this that Okay, this is on screen now On your calculator screen now. So this will be 0.84 2 to 4. Same way this is a P two now. So with P two if I just multiply five by three I get the next value which will be 0.140374 then 0.175 467 Then 0.175 467. And you think how can these two probabilities equal? We'll look at here Here five x 5 so it will cancel. So whatever is pay for that only will become pre fight. That's how these two are equal. And then the final one is 0.146 2 to 3. So I hope you could understand this. Let me know if you have any questions.


Similar Solved Questions

5 answers
(1+74) tan A tan B explicitly HINT: Use the identitytan( A B) = (1 ++2) tan Atan BSolve
(1+74) tan A tan B explicitly HINT: Use the identitytan( A B) = (1 ++2) tan Atan B Solve...
5 answers
Luc iud ~e Eiple iXenaled_{~ex e bowkded 9+82722 22x lr Vo cubte aGe AtE ~Gl uic(
luc iud ~e Eiple iXenaled_{~ex e bowkded 9+82722 22x lr Vo cubte aGe AtE ~Gl u ic(...
5 answers
Classify the graph of the equation as circle; parabola, an ellipse, or a hyperbola __8r- 4y28y _ 7 =0
Classify the graph of the equation as circle; parabola, an ellipse, or a hyperbola __ 8r- 4y2 8y _ 7 =0...
5 answers
Consider the function:(2+1)2 sin (4) , for I€ (-0,-1) 6r+ % for T el-1,0]f()sin(az)for T € (0.0)Find all possible values of a and b that make f(r) continuous at x =and #
Consider the function: (2+1)2 sin (4) , for I€ (-0,-1) 6r+ % for T el-1,0] f() sin(az) for T € (0.0) Find all possible values of a and b that make f(r) continuous at x = and #...
5 answers
Questione Draw the fepeating scpmcnt for the polymer forrned from the rcactions using the given pnonoincttrudcal(b) HOCrCH?BCH CH-ACH Br NaoHLgl -Natta catelutarminoHOCH CH AHGive thc tionoanctfs) required anthei euch of thc follo-Ing palcmncnM
Questione Draw the fepeating scpmcnt for the polymer forrned from the rcactions using the given pnonoinctt rudcal (b) HO CrCH? BCH CH-ACH Br NaoH Lgl -Natta catelut armino HOCH CH AH Give thc tionoanctfs) required anthei euch of thc follo-Ing palcmncn M...
5 answers
15. [-/6 Points]DETAILSROGACALCET4 13.5.005Calculate the velocity and acceleration vectors and the speed at the time indicatedr(0)sin(0) , cos(0) , cos(90)) , 0 =Submit Answer
15. [-/6 Points] DETAILS ROGACALCET4 13.5.005 Calculate the velocity and acceleration vectors and the speed at the time indicated r(0) sin(0) , cos(0) , cos(90)) , 0 = Submit Answer...
5 answers
What is the difference between a gene and a chromosome?
What is the difference between a gene and a chromosome?...
1 answers
Two point charges are on the $x$ axis. Charge 1 is $+q$ and is located at $x=-1.0 \mathrm{m} ;$ charge 2 is $-2 q$ and is located at $x=1.0 \mathrm{m}$ Make sketches of the equipotential surfaces for this system (a) out to a distance of about $2.0 \mathrm{m}$ from the origin and (b) far from the origin. In each case, indicate the direction in which the potential increases.
Two point charges are on the $x$ axis. Charge 1 is $+q$ and is located at $x=-1.0 \mathrm{m} ;$ charge 2 is $-2 q$ and is located at $x=1.0 \mathrm{m}$ Make sketches of the equipotential surfaces for this system (a) out to a distance of about $2.0 \mathrm{m}$ from the origin and (b) far from the ori...
5 answers
5 2.Solve the 5 Attempts 5 4un+1 2911 Following nons 4u7 I| 4n , 5 homogeneous difference equation wi 5 difference equation Available with 8 th ininai ininal ati2am Icond conditions: Inons Dec 2 at11.5 Wdb LAEA1Previous
5 2.Solve the 5 Attempts 5 4un+1 2911 Following nons 4u7 I| 4n , 5 homogeneous difference equation wi 5 difference equation Available with 8 th ininai ininal ati2am Icond conditions: Inons Dec 2 at11.5 Wdb LAEA 1Previous...
5 answers
Find the circumference of thecircle x2 + y2 = 4 by using the formula for arclength of a curve. Verify your answer by using the circumferenceformula for a circle.
Find the circumference of the circle x2 + y2 = 4 by using the formula for arc length of a curve. Verify your answer by using the circumference formula for a circle....
5 answers
The equation for the curve of the solution volume V inmL as a function of moles (n) with 1000.0 g of water was found toreproduce the experimental data for NaOH solutions very well, andis given below. V= 1002.03 - 8.66n + 5.65n3/2 -0.275n2Find the partial molar volume for a 2 molalsolution.
The equation for the curve of the solution volume V in mL as a function of moles (n) with 1000.0 g of water was found to reproduce the experimental data for NaOH solutions very well, and is given below. V= 1002.03 - 8.66n + 5.65n3/2 - 0.275n2 Find the partial molar volume for a 2 molal solution....
5 answers
Question 9 (1 point) What is the relationship between these two structures?BrDiastereomersb) Constitutional isomersIdentical structuresEnantiomers
Question 9 (1 point) What is the relationship between these two structures? Br Diastereomers b) Constitutional isomers Identical structures Enantiomers...
4 answers
Find the value of x if[5 21--[: ;+[2 :OAI =-6 B.I = 6 C.* = -3 D.I = 3 E.I= 0
Find the value of x if [5 21--[: ;+[2 : OAI =-6 B.I = 6 C.* = -3 D.I = 3 E.I= 0...
5 answers
Let J be a suitable functional ofthe formJly] = f Fo"+v)vi+6)= dr_where F F(z? + y?) is some sufficiently smooth function of z2 + y?. Transform the functional into polar coordinates where 1' COS 0, ! rsin 0 and find the general form of the extremals in terms of the unknown function F and the coordinates r and
Let J be a suitable functional ofthe form Jly] = f Fo"+v)vi+6)= dr_ where F F(z? + y?) is some sufficiently smooth function of z2 + y?. Transform the functional into polar coordinates where 1' COS 0, ! rsin 0 and find the general form of the extremals in terms of the unknown function F and...
5 answers
MM2 mA6 [
MM 2 mA 6 [...
5 answers
You are exploting the planct Zorp in thc Muccus Galaxy in tie yeat 3230_You cncounter 4 strange crcature during onc of your scouting missions and dccide t0 rccord sote dati on thc number of thcm Jou scc; (Your table 1s below: ) What kind of gronth Is thc creature population exhibiting and how do you know?DaysPopulation154 346 779
You are exploting the planct Zorp in thc Muccus Galaxy in tie yeat 3230_You cncounter 4 strange crcature during onc of your scouting missions and dccide t0 rccord sote dati on thc number of thcm Jou scc; (Your table 1s below: ) What kind of gronth Is thc creature population exhibiting and how do yo...
5 answers
1__ How many moles of sulfur are in 53.7 grams of sulfur?2. Calculate the molar mass of CuSO4 xneloof 13.2 mol of CaCh Calculate mass in grams 3.Hoii in 16.4 g of CoHnO6 number of moles 4 Calculatecan with a inum
1__ How many moles of sulfur are in 53.7 grams of sulfur? 2. Calculate the molar mass of CuSO4 xnelo of 13.2 mol of CaCh Calculate mass in grams 3. Hoii in 16.4 g of CoHnO6 number of moles 4 Calculate can with a inum...

-- 0.020401--