Question

1) Let X and Y be a bivariate random variables denoting the number of cars and buses, respectively, lined up at a stop light at a given point in time. Suppose that their joint probability density function is given by the following table | y x | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | 0 | 0.025 | 0.050 | 0.125 | 0.150 | 0.100 | 0.050 | | 1 | 0.015 | 0.030 | 0.075 | 0.090 | 0.060 | 0.030 | | 2 | 0.010 | 0.020 | 0.050 | 0.060 | 0.040 | 0.020 | Calculate the following values: i) Probability that there are exactly 4 cars and no buses ii) Probability that there are exactly 5 cars iii) Probability that there is exactly 1 bus iv) Probability that there is at most 3 cars and at least one bus v) the correlation coefficient ?(X,Y)

          1) Let X and Y be a bivariate random variables denoting the number of cars and buses, respectively, lined up at a stop light at a given point in time. Suppose that their joint probability density function is given by the following table

| y  x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 0.025 | 0.050 | 0.125 | 0.150 | 0.100 | 0.050 |
| 1 | 0.015 | 0.030 | 0.075 | 0.090 | 0.060 | 0.030 |
| 2 | 0.010 | 0.020 | 0.050 | 0.060 | 0.040 | 0.020 |

Calculate the following values:
i) Probability that there are exactly 4 cars and no buses
ii) Probability that there are exactly 5 cars
iii) Probability that there is exactly 1 bus
iv) Probability that there is at most 3 cars and at least one bus
v) the correlation coefficient ?(X,Y)

1) Let X and Y be a bivariate random variables denoting the number of cars and buses, respectively, lined up at a stop light at a given point in time. Suppose that their joint probability density function is given by the following table

| y x | 0 | 1 | 2 | 3 | 4 | 5 |
|—|—|—|—|—|—|—|
| 0 | 0.025 | 0.050 | 0.125 | 0.150 | 0.100 | 0.050 |
| 1 | 0.015 | 0.030 | 0.075 | 0.090 | 0.060 | 0.030 |
| 2 | 0.010 | 0.020 | 0.050 | 0.060 | 0.040 | 0.020 |

Calculate the following values:
i) Probability that there are exactly 4 cars and no buses
ii) Probability that there are exactly 5 cars
iii) Probability that there is exactly 1 bus
iv) Probability that there is at most 3 cars and at least one bus
v) the correlation coefficient ?(X,Y)

Added by Mikayla C.

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