Question

People at a shopping mall were asked how many times they went to the movies in the last month. The results are listed in the table below. Use that information for parts a and b. х 0 1 P(x) 0.453 0.102 0.239 0.071 0.249 2 3 4 a. Does the table represent a probability distribution? (2 points) A. Yes B. No b. If "yes", give the mean (1) and standard deviation (o), if "no", give at least one requirement that is not met. (3 points)

Answer 1

Son- let X : Number of times went to the movie in last month. Given x per) table; o 0.453 0.102 2. 0.239 3 0.071 4 0. 24.9 @. To check it is probability is probability distribution or not We need check, : Non- negativity per) Notice that P(x) > 0 &x=0,1,2, 3, 4 - Non- negativity holds. Doro ii) Total probability should be unity .. P( x = c) + P(x-1) + P : a) + PC r=3) + DEX:4) 0.453+ 0.102+0.239+ 0.071 + 0.249 - 1114 >1. Since Total probability is greater than 1, it is not a probability distribution 6 NO!, it is not the probability distribution It does not fulfil following requirement; From given table, P(x=0) +pla=1) + Be2=2) + P(1=3) + Pl x=4) Total Probability 0.453+ 0.102 + 0.239+ 0.071 + 0.249 l. 114 > 1 that for any probability distribuſion, total probability We know should be Thus, low of one total_pobability does not held Scanned with CamScanner