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  4. Given below is the distribution of a random variable X X=x 1 2 3 4 P(X=x) λ 2λ 3λ 4λ If α=P(X<3) and β=P(X>2), then α: β=

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Q. Given below is the distribution of a random variable $X$
$X=x$ 1 2 3 4
$P(X=x)$ $\lambda$ $2\lambda$ $3\lambda$ $4\lambda$

If $\alpha=P(X<3)$ and $\beta=P(X>2)$, then $\alpha: \beta=$

AP EAMCETAP EAMCET 2017

Solution:

Clearly $\alpha=P(x<3)=P(x=1)+P(x=2)=3 \lambda$
and $\beta=P(x>2)=P(x=3)+P(x=4)=7 \lambda$
$\therefore \alpha: \beta=3: 7$