Question

6) Let X and Y be discrete random variables with joint probability distribution given by the following table: x -3 2 4 +---------+ 1 |0.1 k 0.2| y | | 3 |0.3 0.1 0.1| +---------+ a) Determine the appropriate value for k ? ? so that is is a valid joint probability distribution. b) Find the following probabilities: P(X = 2, Y = 3) P(X ? 2, Y = 1) P(X < 2, Y = 1) P(X > 3, Y ? 3) P(X = 2) P(Y ? 3)

          6) Let X and Y be discrete random variables with joint probability distribution given by the following table:

     x
   -3  2  4
  +---------+
1 |0.1 k  0.2|
y |         |
3 |0.3 0.1 0.1|
  +---------+

a) Determine the appropriate value for k ? ? so that is is a valid joint probability distribution.

b) Find the following probabilities:
P(X = 2, Y = 3)          P(X ? 2, Y = 1)          P(X < 2, Y = 1)
P(X > 3, Y ? 3)          P(X = 2)                 P(Y ? 3)

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6) Let X and Y be discrete random variables with joint probability distribution given by the following table:

x
-3 2 4
+———+
1 |0.1 k 0.2|
y | |
3 |0.3 0.1 0.1|
+———+

a) Determine the appropriate value for k ? ? so that is is a valid joint probability distribution.

b) Find the following probabilities:
P(X = 2, Y = 3) P(X ? 2, Y = 1) P(X < 2, Y = 1)
P(X > 3, Y ? 3) P(X = 2) P(Y ? 3)

Added by Jeffrey B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/07/2023

Step 1

For this, we need to make sure that the sum of all probabilities in the table is equal to 1. The table looks like this: | | Y=1 | Y=2 | Y=3 | |---|-----|-----|-----| | X=1 | 0.1 | 0.2 | 0.3 | | X=2 | 0.1 | 0.1 | k | Now, let's sum up all the probabilities Show more…

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6) Let X and Y be discrete random variables with joint probability distribution given by the following table: x: -3, 2, 4 y=1: 0.1, k, 0.2 y=3: 0.3, 0.1, 0.1 a) Determine the appropriate value for k ∈ ℑ so that is is a valid joint probability distribution. b) Find the following probabilities: P(X = 2, Y = 3) P(X ≤ 2, Y = 1) P(X < 2, Y = 1) P(X > 3, Y ≤ 3) P(X = 2) P(Y ≤ 3)

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