Question

Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 for the next five years. Considering the experience of VCR users, the following distribution of maintenance expenses for the next five years is formed.

The expected value of maintenance cost is :

• A. Rs. 800
• B. Rs. 770
• C. Rs. 700
• D. Rs. 900

Hint:

When adding up long decimal products mentally, combine terms that share clean sums. For example, $125 + 125 = 250$, and $150 + 150 = 300$. Grouping elements makes calculation smooth and less prone to simple errors under test pressure!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a discrete probability distribution table outlining various potential maintenance costs (random variable $x_i$) alongside their historical probabilities of occurrence ($p_i$). We need to calculate the mathematical expected value ($E(x)$) of this distribution.

Step 2: Key Formula or Approach:
The expected value of a discrete random variable is the weighted average of all possible values, calculated by taking the sum of the products of each value and its corresponding probability: $$ E(x) = \sum p_i x_i $$

Step 3: Detailed Explanation:
Let's list the paired value and probability products systematically from the distribution context:

• For expense 0: $0 \times 0.35 = 0$

• For expense 500: $500 \times 0.25 = 125$

• For expense 1000: $1000 \times 0.15 = 150$

• For expense 1500: $1500 \times 0.10 = 150$

• For expense 2000: $2000 \times 0.08 = 160$

• For expense 2500: $2500 \times 0.05 = 125$

• For expense 3000: $3000 \times 0.02 = 60$
Now, sum these individual expected component contributions together to find the total: $$ E(x) = 0 + 125 + 150 + 150 + 160 + 125 + 60 $$ $$ E(x) = 275 + 150 + 160 + 125 + 60 $$ $$ E(x) = 425 + 160 + 125 + 60 $$ $$ E(x) = 585 + 125 + 60 = 710 + 60 = 770 $$ The statistically expected long-term maintenance expense is Rs. 770.

Step 4: Final Answer:
The expected value of the maintenance cost is Rs. 770, which corresponds to option (B).