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JEE Main 20257 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
7 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 7 April · Evening Shift · Mathematics · Probability

Let a random variable X take values 0,1,2,3 with P(X=0)=P(X=1)=p,...

Let a random variable X take values 0,1,2,30,1,2,3 with P(X=0)=P(X=1)=p,P(X=2)=P(X=3)\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)=\mathrm{p}, \mathrm{P}(\mathrm{X}=2)=\mathrm{P}(\mathrm{X}=3) and E(X2)=2E(X)\mathrm{E}\left(\mathrm{X}^2\right)=2 \mathrm{E}(\mathrm{X}). Then the value of 8p−18 \mathrm{p}-1 is :

Options

  1. A0
  2. B2
  3. C1
  4. D3

Correct answer

B. 2

Step-by-step solution

2p+2q=12p+qE(x2)=∑i=03xi2p(xi)=0⋅p+1⋅p+4⋅q+9q=p+13qE(x)=∑i=03xi2p(xi)=0⋅p+1⋅p+2q+3q=p+5qp+13q=2(p+5q)p=3q So, q=18p=38 So, 8p−1=2 Option (2) \begin{aligned} & 2 p+2 q=\frac{1}{2} \\ & p+q \\ & E\left(x^2\right)=\sum_{i=0}^3 x_i^2 p\left(x_i\right)=0 \cdot p+1 \cdot p+4 \cdot q+9 q \\ & =p+13 q \\ & E(x)=\sum_{i=0}^3 x_i^2 p\left(x_i\right)=0 \cdot p+1 \cdot p+2 q+3 q=p+5 q \\ & p+13 q=2(p+5 q) \\ & p=3 q \\ & \text{ So, } q=\frac{1}{8} & p=\frac{3}{8} \quad \\ & \text{ So, } 8 p-1=2 \quad \text{ Option (2) }\end{aligned}
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