Question
Patients receiving artificial knees often experience painafter surgery. The pain is measured on a subjective scale withpossible values of 1 to 5. Assume that X is a random variablerepresenting the pain score for a randomly elected patient. Thefollowing table gives part of the probability distribution forX. X 1 2 3 4 5 P(X) .1 .2 .3 .3 a. Find P(X=5) b. Find the probability that the pain score is less than3. c. Find the mean for this distribution. d. Find the variance for this distribution. e. Find the standard deviation for this distribution. f. Suppose the pain scores for two randomly selected patientsare recorded. Let Y be the random variable representing the sum ofthe two scores. Find the mean of Y. g. Find the standard deviation of Y. Please show work! THANKS!!!!! Patients receiving artificial knees often experience painafter surgery. The pain is measured on a subjective scale withpossible values of 1 to 5. Assume that X is a random variablerepresenting the pain score for a randomly elected patient. Thefollowing table gives part of the probability distribution forX. X 1 2 3 4 5 P(X) .1 .2 .3 .3 a. Find P(X=5) b. Find the probability that the pain score is less than3. c. Find the mean for this distribution. d. Find the variance for this distribution. e. Find the standard deviation for this distribution. f. Suppose the pain scores for two randomly selected patientsare recorded. Let Y be the random variable representing the sum ofthe two scores. Find the mean of Y. g. Find the standard deviation of Y. Please show work! THANKS!!!!!
Explanation / Answer
a. the sum of all the probabilities must be 1, therefore, 1-all the probabilities given to you = 0.1 b. P(X=1) + P(X=2) = 0.3 c. do a weighted average: (0.1)(1)+(0.2)(2)+(0.3)(3)... and soon = 3.1/5 (i don't have a calculator near me!) d. the variance formula ispi*(xi-)2 where mu is theaverage.. so to start you off (because i am not near acalculator!), do this: 0.1*(1-avg from partC)2+0.2*(2-avg from part C)2+0.3*(3-avg frompart C)2+0.3*(4-avg from part C)2+0.2*(2-avgfrom part C)2+0.1(5-avg from part C)2 e.take the square root of your answer from part d. this is thestandard deviation f. ok to solve for y, imagine the first person feels a pain of1. then the other person can feel pain of 1, 2, 3, 4, or 5. imagine the first person feels a pain of 2. the other personcan feel pain of 1, 2, 3, 4, or 5. once you do this all the way up til the first person havingpain of 5, you will see that they will add up to 2 1/25 times. theywill add up to 3 2/25 times, add up to 4 3/25 times, add up to 54/25 times, add up to 6 5/25 times... and then add up to 7 4/25times and so on until them adding up to 10 occurs 1/25 times. soit's a distribution that will peak in the middle! to find the mean, find the weighted avg like in part c abovewith the x/25 probabilities times the probability of pain = 1, 2,3, 4,...,10. g. find the variance, as done above in part d. take the squareroot and tah-dah! standard deviation! thanks for the points :D e.take the square root of your answer from part d. this is thestandard deviation f. ok to solve for y, imagine the first person feels a pain of1. then the other person can feel pain of 1, 2, 3, 4, or 5. imagine the first person feels a pain of 2. the other personcan feel pain of 1, 2, 3, 4, or 5. once you do this all the way up til the first person havingpain of 5, you will see that they will add up to 2 1/25 times. theywill add up to 3 2/25 times, add up to 4 3/25 times, add up to 54/25 times, add up to 6 5/25 times... and then add up to 7 4/25times and so on until them adding up to 10 occurs 1/25 times. soit's a distribution that will peak in the middle! to find the mean, find the weighted avg like in part c abovewith the x/25 probabilities times the probability of pain = 1, 2,3, 4,...,10. g. find the variance, as done above in part d. take the squareroot and tah-dah! standard deviation! thanks for the points :D