Question

number of cars probability 0 0.09 1 0.36 2 0.35 3 0.13 4 0.05 5 0.02 choose an american household at random. what is the expected number of cars for that household?

Explanation:

Step1: Recall the formula for expected value

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

Step2: Calculate each term \( x_{i}P(x_{i}) \)

• For \( x = 0 \), \( P(x)=0.09 \), so \( 0\times0.09 = 0 \)
• For \( x = 1 \), \( P(x)=0.36 \), so \( 1\times0.36=0.36 \)
• For \( x = 2 \), \( P(x)=0.35 \), so \( 2\times0.35 = 0.7 \)
• For \( x = 3 \), \( P(x)=0.13 \), so \( 3\times0.13=0.39 \)
• For \( x = 4 \), \( P(x)=0.05 \), so \( 4\times0.05 = 0.2 \)
• For \( x = 5 \), \( P(x)=0.02 \), so \( 5\times0.02=0.1 \)

Step3: Sum up the terms

\( E(X)=0 + 0.36+0.7 + 0.39+0.2+0.1\)
\( E(X)=1.75\)

Answer:

\( 1.75 \)