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(X2), then α: β=

Question

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= (A) 2: 5 (B) 3: 4 (C) 4: 5 (D) 3: 7

Tardigrade Admin · Accepted Answer

Clearly α=P(x<3)=P(x=1)+P(x=2)=3 λ and β=P(x>2)=P(x=3)+P(x=4)=7 λ ∴ α: β=3: 7

$X = x$	1	2	3	4
$P (X = x)$	$λ$	$2 λ$	$3 λ$	$4 λ$

Q. Given below is the distribution of a random variable $X$

$X = x$ 1 2 3 4

$P (X = x)$ $λ$ $2 λ$ $3 λ$ $4 λ$

If $α = P (X < 3)$ and $β = P (X > 2)$ , then $α : β =$

2 : 5

3 : 4

4 : 5

3 : 7

Clearly $α = P (x < 3) = P (x = 1) + P (x = 2) = 3 λ$
and $β = P (x > 2) = P (x = 3) + P (x = 4) = 7 λ$
$∴ α : β = 3 : 7$

Q. 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=