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BITSAT 2024Paper 2

Exam: BITSAT
Year: 2024
Paper: Paper 2
Subject: Mathematics
Chapter: Probability

BITSAT 2024 · Paper 2 · Mathematics · Probability

Given below is the distribution of a random variable X If α=P(X 2)...

Given below is the distribution of a random variable

X

Given below is the distribution of a random variable X If α=P(X 2) , then α: β=

If

\alpha=\mathrm{P}(X < 3)

and

\beta=\mathrm{P}(X>2)

, then

\alpha: \beta=

Options

A $2: 5$
B $3: 4$
C $4: 5$
D $3: 7$

Correct answer

D. $3: 7$

Step-by-step solution

For a distribution of random variable

x

,

\alpha=P\left(X^6 < 3\right)=P\left(X^6=1\right)+P\left(X^6=2\right)

\begin{aligned} & =\lambda+2 \lambda=3 \lambda \\ & \text{\text{ and } } \beta=P\left(X^6 < 2\right)=P\left(X^6=3\right)+P\left(X^6=4\right) \\ & =3 \lambda+4 \lambda=3 \lambda \\ & \therefore \quad \alpha: \beta=3: 7\end{aligned}

$$

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