Random variables and have the following joint probability distribution.

1 2 3
1 0.2 0.4 0.05
2 0.15 0.10 0.10

Find (write it up to second decimal place).

Question

Random variables  and  have the following joint probability distribution.

1	2	3
	1	0.2	0.4	0.05
2	0.15	0.10	0.10

Find  (write it up to second decimal place).

BlackTom AI · Accepted Answer

We begin by identifying the marginal probabilities for X from the joint distribution.
First, sum the probabilities for X = 1 across all Y: 0.2 + 0.4 + 0.05 = 0.65. This gives P(X = 1) = 0.65.
Next, sum the probabilities for X = 2 across all Y: 0.15 + 0.10 + 0.10 = 0.35. This yields P(X = 2) = 0.35.
Now, recall that the expected value of X is E[X] = Σ x · P(X = x). Since X takes values 1 and 2, we compute:
E[X] = 1 · P(X = 1) + 2 · P(X = 2) = 1 · 0.65 + 2 · 0.35.
Carrying out the arithmetic: 1 · 0.65 = 0.65 and 2 · 0.35 = 0.70, so E[X] = 0.65 + 0.70 = 1.35.
When rounding to two decimal places, the result remains 1.35. 
Thus, the expected value E(X) is 1.35.

AMS 310 Homework 7

Random variables and have the following joint probability distribution. 1 2 3 1 0.2 0.4 0.05 2 0.15 0.10 0.10 Find (write it up to second decimal place).

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