Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables. Number ofVisits (Y) Years in School (X) 1 2 3 4 0 1 2 0.07 0.13 0.04 0.05 0.11 0.04 0.03 0.17 0.09 0.02 0.15 0.10 a. Find the probability that a randomly chosen student has not visited a museum in the last year.b. Find the means of the random variables X and Y.c. Find and interpret the covariance between the random variables X and Y.
Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables. Number ofVisits (Y) Years in School (X) 1 2 3 4 0 1 2 0.07 0.13 0.04 0.05 0.11 0.04 0.03 0.17 0.09 0.02 0.15 0.10 a. Find the probability that a randomly chosen student has not visited a museum in the last year.b. Find the means of the random variables X and Y.c. Find and interpret the covariance between the random variables X and Y.
Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables. Number ofVisits (Y) Years in School (X) 1 2 3 4 0 1 2 0.07 0.13 0.04 0.05 0.11 0.04 0.03 0.17 0.09 0.02 0.15 0.10 a. Find the probability that a randomly chosen student has not visited a museum in the last year.b. Find the means of the random variables X and Y.c. Find and interpret the covariance between the random variables X and Y.
Students in a college were classified according to years in school (X) and number of visits to a museum in the last year (Y = 0 for no visits, 1 for one visit, 2 for more than one visit). The joint probabilities in the accompanying table were estimated for these random variables.
Number of Visits (Y)
Years in School (X)
1
2
3
4
0
1
2
0.07
0.13
0.04
0.05
0.11
0.04
0.03
0.17
0.09
0.02
0.15
0.10
a. Find the probability that a randomly chosen student has not visited a museum in the last year. b. Find the means of the random variables X and Y. c. Find and interpret the covariance between the random variables X and Y.
Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.
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