Question

select the correct answer.

x	probability
1	0.1
2	0.4
3	0.2
4	0.1

the probability distribution of x, a discrete random variable, is given in the table. what is the expected value of x?

a. 0.8
b. 1.9
c. 2
d. 5

Explanation:

Step1: Recall the formula for expected value of a discrete random variable

The expected value \( E(X) \) of a discrete random variable \( X \) is calculated as \( E(X)=\sum_{i} x_i P(x_i) \), where \( x_i \) are the possible values of \( X \) and \( P(x_i) \) are their corresponding probabilities.

Step2: Calculate each term \( x_i P(x_i) \)

• For \( x = 0 \): \( 0\times0.2 = 0 \)
• For \( x = 1 \): \( 1\times0.1 = 0.1 \)
• For \( x = 2 \): \( 2\times0.4 = 0.8 \)
• For \( x = 3 \): \( 3\times0.2 = 0.6 \)
• For \( x = 4 \): \( 4\times0.1 = 0.4 \)

Step3: Sum up all the terms

Add all the calculated terms: \( 0 + 0.1 + 0.8 + 0.6 + 0.4 = 1.9 \)

Answer:

B. 1.9