MAH-CET 2025 — Mathematics PYQ

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Question

MAH-CET 2025 — Mathematics PYQ

MAH-CET | Mathematics | 2025

If the probability distribution function of a random variable X is given by $f (x) = {\frac{1}{7}, 0, am p; \forall1 am p; otherwise l t; x l t; 8$ Then the value of $P(3 < X < 10)$ is

Choose the correct answer:

Explanation

Mathematical Calculation:

1. Given PDF:

f(x) = \begin{cases} \frac{1}{7}, & 1 < x < 8 \\ 0, & \text{otherwise} \end{cases}

2. Probability nikaalne ka formula:

Continuous random variable ke liye probability integral ke barabar hoti hai:

P(3 < X < 10) = \int_{3}^{10} f(x) \, dx

3. Limits ko split karna:

Kyunki function $x = 8$ ke baad $0$ ho jata hai, isliye integral ko do hisson mein todte hain:

P(3 < X < 10) = \int_{3}^{8} f(x) \, dx + \int_{8}^{10} f(x) \, dx

P(3 < X < 10) = \int_{3}^{8} \frac{1}{7} \, dx + \int_{8}^{10} 0 \, dx

4. Integral Solve karna:

P(3 < X < 10) = \left[ \frac{x}{7} \right]_{3}^{8} + 0

P(3 < X < 10) = \frac{8}{7} - \frac{3}{7}

P(3 < X < 10) = \frac{5}{7}

Final Answer:

$P(3 < X < 10)$ ki value $\frac{5}{7}$ hai.