Class 12 Probability · Very Long Answer5 Marksprobability_distributions

Class 12 Maths · Probability · Very Long Answer #84

Select two distinct numbers uniformly from {1,2,3,4,5}. X is their maximum. Find E(X).

✅ Step-by-Step Solution

Final Answer: P(X=2)=1/10; P(X=3)=1/5; P(X=4)=3/10; P(X=5)=2/5. Mean=4.

There are C(5,2)=10 equally likely unordered pairs. The maximum can be 2,3,4,5.
For maximum k, include k and choose its partner from {1,…,k−1}; counts are 1,2,3,4.
The resulting distribution is P(X=2)=1/10; P(X=3)=1/5; P(X=4)=3/10; P(X=5)=2/5. Its nonnegative masses sum to 1.
E(X)=ΣxP(X=x)=(2)(1/10)+(3)(1/5)+(4)(3/10)+(5)(2/5)=4.
P(X=2)=1/10; P(X=3)=1/5; P(X=4)=3/10; P(X=5)=2/5. Mean=4.

[1 mark] There are C(5,2)=10 equally likely unordered pairs. The maximum can be 2,3,4,5.
[1 mark] For maximum k, include k and choose its partner from {1,…,k−1}; counts are 1,2,3,4.
[1 mark] The resulting distribution is P(X=2)=1/10; P(X=3)=1/5; P(X=4)=3/10; P(X=5)=2/5. Its nonnegative masses sum to 1.
[1 mark] E(X)=ΣxP(X=x)=(2)(1/10)+(3)(1/5)+(4)(3/10)+(5)(2/5)=4.
[1 mark] P(X=2)=1/10; P(X=3)=1/5; P(X=4)=3/10; P(X=5)=2/5. Mean=4.

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