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Question
The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.
Then show that P (X ≤ 2) = P (X ≥ 3).
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Solution
P (X ≤ 2) = P(X = 0 ) + P(X = 1)+P(X = 2)
= `(""^5C_0)/2^5 + (""^5C_1)/2^5 + (""^5C_2)/2^5`
= `(""^5C_5)/2^5 + (""^5C_4)/2^5 + (""^5C_3)/2^5` ........[`""^nC_r = ""^nC_n-r`]
= P (X = 5) + P (X = 4) + P (X = 3)
= P (X ≥ 3 )
∴ P (X ≤ 2) = P (X ≥ 3).
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