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Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions2 Marks
MCQ
The following table represents a probability distribution for a random variable X :
$\mathrm{X}=\boldsymbol{x}$01234
P($\mathrm{X}=\boldsymbol{x}$)k2k3k4k5k
Then the value of k is
  • A
    $\frac{1}{2}$
  • B
    $\frac{1}{6}$
  • C
    $\frac{1}{3}$
  • ✓
    $\frac{1}{9}$
✓

Answer

Correct option: D.
$\frac{1}{9}$
(D)
$Since \sum_{x=0}^4 \mathrm{P}(\mathrm{X}=x)=1$
$\begin{aligned} & \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+2 \mathrm{k}+\mathrm{k}=1 \\ & \Rightarrow 9 \mathrm{k}=1 \Rightarrow \mathrm{k}=\frac{1}{9}\end{aligned}$

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