ProbabilityMTP Nov 19Question 3402 of 170
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If a random variable X\displaystyle X assumes the values x1,x2,x3,x4\displaystyle x_1, x_2, x_3, x_4 with corresponding probabilities, P1,P2,P3,P4\displaystyle P_1, P_2, P_3, P_4 then the expected value of X\displaystyle X is

Options

AP1+P2+P3+P4\displaystyle P_1 + P_2 + P_3 + P_4
Bx1P1+x2P2+x3P3+x4P4\displaystyle x_1 P_1 + x_2 P_2 + x_3 P_3 + x_4 P_4
Cx1P2+x2P3+x3P4+x4P1\displaystyle x_1 P_2 + x_2 P_3 + x_3 P_4 + x_4 P_1
DNone
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Correct Answer

Option bx1P1+x2P2+x3P3+x4P4\displaystyle x_1 P_1 + x_2 P_2 + x_3 P_3 + x_4 P_4

All Options:

  • AP1+P2+P3+P4\displaystyle P_1 + P_2 + P_3 + P_4
  • Bx1P1+x2P2+x3P3+x4P4\displaystyle x_1 P_1 + x_2 P_2 + x_3 P_3 + x_4 P_4
  • Cx1P2+x2P3+x3P4+x4P1\displaystyle x_1 P_2 + x_2 P_3 + x_3 P_4 + x_4 P_1
  • DNone

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

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