1. A researcher suspected that the number of between-meal snacks eaten by students in a day during final examinations might depend on the number of tests that a student had to take on that day. The following table shows joint probabilities, estimated from a survey. Number of Number of Tests (X) Snacks (Y) 1 2 3 0.07 0.09 0.06 0.01 1 0.07 0.06 0.07 0.01 2 0.06 0.07 0.14 0.03 3 0.02 0.04 0.16 0.04 a. Find the mean number of tests taken by students on that day. b. Find the mean number of snacks eaten by students on that day. c. Find and interpret the conditional probability function of Y, given that X = 3. d. Find the covariance between X and Y. e. Are the number of snacks and number of tests independent of each other?

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1. A researcher suspected that the number of between-meal snacks eaten by students in a day during final
examinations might depend on the number of tests that a student had to take on that day. The following table
shows joint probabilities, estimated from a survey.
Number of
Number of Tests (X)
Snacks (Y)
1
2
3
0.07
0.09
0.06
0.01
0.07
0.06
0.07
0.01
2
0.06
0.07
0.14
0.03
3
0.02
0.04
0.16
0.04
a. Find the mean number of tests taken by students on that day.
b. Find the mean number of snacks eaten by students on that day.
c. Find and interpret the conditional probability function of Y, given that X = 3.
d. Find the covariance between X and Y.
e. Are the number of snacks and number of tests independent of each other?
Transcribed Image Text:1. A researcher suspected that the number of between-meal snacks eaten by students in a day during final examinations might depend on the number of tests that a student had to take on that day. The following table shows joint probabilities, estimated from a survey. Number of Number of Tests (X) Snacks (Y) 1 2 3 0.07 0.09 0.06 0.01 0.07 0.06 0.07 0.01 2 0.06 0.07 0.14 0.03 3 0.02 0.04 0.16 0.04 a. Find the mean number of tests taken by students on that day. b. Find the mean number of snacks eaten by students on that day. c. Find and interpret the conditional probability function of Y, given that X = 3. d. Find the covariance between X and Y. e. Are the number of snacks and number of tests independent of each other?
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