Question
In a binomial distribution, the mean is 4 and variance is 3 . Then, its mode is
BITSAT
Mathematics
Probability
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 5
- B. 6
- C. 4
- D. None of these
Answer
C. 4
Step-by-step solution
aligned Mean & =n p=4 \\ Variance & =n p q=3 \\ q & = 3 4 aligned and p=1-q=1- 3 4 = 1 4 n=16 Now, Mode of Binomial distribution is given by (n+1) P Case IIf (n+1) P= Integer (I), then Mode =\ I, I-1\ Case II If (n+1) P Integer (I+f), then Mode =\ I\ aligned (n+1) P & =(16+1) 1 4 \\ & = 17 4 =4.25 \\ & =4+0.25 \\ Mode & =4 aligned
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