MAH-CET 2025 — Mathematics PYQ

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Question

MAH-CET 2025 — Mathematics PYQ

MAH-CET | Mathematics | 2025

In a binomial distribution, mean and variance are 12 and 4 respectively. the parameters of the distribution are

Choose the correct answer:

Explanation

Mathematical Calculation:

1. Given Data:

Mean ( $np$ ) = $12$

Variance ( $npq$ ) = $4$

2. $q$ ki value nikaalna:

Humein pata hai ki $\frac{\text{Variance}}{\text{Mean}} = q$

q = \frac{npq}{np} = \frac{4}{12}

q = \frac{1}{3}

3. $p$ ki value nikaalna:

Kyunki $p + q = 1$ hota hai:

p = 1 - q

p = 1 - \frac{1}{3}

p = \frac{2}{3}

4. $n$ ki value nikaalna:

Mean ke formula ( $np = 12$ ) mein $p$ ki value rakhne par:

n \times \frac{2}{3} = 12

2n = 12 \times 3

2n = 36

n = 18

Final Answer:

Binomial distribution ke parameters hain:

n = 18, \quad p = \frac{2}{3}