Question
A random variable X takes values 0,1,2,3 with probabilities 2 a+1 30 , 8 a-1 30 , 4 a+1 30 , b respectively, where a , b R . Let and respectively be the mean and standard deviation of X such that ^ 2 + ^ 2 =2. Then a b is equal to :
JEE Main
Mathematics
Probability
2026
JEE Main 2026 (21 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 12
- B. 30
- C. 60
- D. 3
Answer
C. 60
Step-by-step solution
Sum of probabilities = 1: 2a+1+8a-1+4a+1 30 + b = 1 b = 29-14a 30 . ^2 + ^2 = E(X^2) = 2. E(X^2) = 8a-1 30 + 4(4a+1) 30 + 9(29-14a) 30 = -102a + 264 30 = 2. -102a + 264 = 60 a = 2. b = 29 - 28 30 = 1 30 . a b = 2 1/30 = 60.
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