Class 12 Probability · Long Answer3 Marksexpectation
Class 12 Maths · Probability · Long Answer #69
X takes 0,1,2,3 with P(0)=P(1)=p and P(2)=P(3)=a. Given E(X²)=2E(X), find p.
✅ Step-by-Step Solution
Final Answer: p=3/8; a=1/8
- Normalization gives 2p+2a=1.
- E(X)=p+5a and E(X²)=p+13a. The moment relation gives p+13a=2p+10a, hence p=3a.
- Then 2(3a)+2a=1 gives a=1/8 and p=3/8.
- The probabilities are 3/8,3/8,1/8,1/8, all valid; hence p=3/8.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Normalization gives 2p+2a=1.
- [1 mark] E(X)=p+5a and E(X²)=p+13a. The moment relation gives p+13a=2p+10a, hence p=3a.
- [1 mark] Then 2(3a)+2a=1 gives a=1/8 and p=3/8.
- [0.5 marks] The probabilities are 3/8,3/8,1/8,1/8, all valid; hence p=3/8.
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