A random variable X has the following probability distribution: X… - Vidyadip

MCQ

A random variable X has the following probability distribution:

$X = x$	0	1	2	3	4	5	6
$P(X = x)$	k	3k	5k	7k	9k	11k	13k

Then, the value of $\mathrm{P}(0<\mathrm{X}<4)$ is

A
$\frac{11}{49}$
✓
$\frac{15}{49}$
C
$\frac{20}{49}$
D
$\frac{40}{49}$

✓

Answer

Correct option: B.

$\frac{15}{49}$

(B)
$\text {Since} \sum_{x=0}^6 \mathrm{P}(\mathrm{X}=x)=1,$
$\begin{aligned} & \mathrm{k}+3 \mathrm{k}+5 \mathrm{k}+7 \mathrm{k}+9 \mathrm{k}+11 \mathrm{k}+13 \mathrm{k}=1 \\ & \Rightarrow 49 \mathrm{k}=1 \Rightarrow \mathrm{k}=\frac{1}{49} \\ & \therefore \mathrm{P}(0<\mathrm{X}<4) \\ & =\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)+\mathrm{P}(\mathrm{X}=3) \\ &=3 \mathrm{k}+5 \mathrm{k}+7 \mathrm{k}=15 \mathrm{k}=\frac{15}{49}\end{aligned}$

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