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Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions2 Marks
MCQ
A random variable X has the following probability distribution:
$X = x$-2-10123
P$(X = x$)0.1k0.22k0.3k
Then, the expected value of X is
  • A
    0.6
  • B
    0.5
  • C
    0.7
  • ✓
    0.8
✓

Answer

Correct option: D.
0.8
(D)
The sum of all the probabilities in a probability distribution is always unity.
$\begin{array}{ll}\therefore 0.1+\mathrm{k}+0.2+2 \mathrm{k}+0.3+\mathrm{k}=1 \\ \Rightarrow 0.6+4 \mathrm{k}=1 \\ \Rightarrow 4 \mathrm{k}=0.4 \\ \Rightarrow \mathrm{k}=0.1 \\\therefore \mathrm{E}(\mathrm{X})=\sum x_i \cdot \mathrm{P}\left(x_i\right) \\ =(-2)(0.1)+(-1)(0.1)+0(0.2)+1(2 \times 0.1)+2(0.3)+3(0.1)=0.8\end{array}$

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