MHT CET · Maths · Probability
For the probability distribution
The Expected value of X is
- A 1.45
- B 1.55
- C 2.45
- D 2.55
Answer & Solution
Correct Answer
(C) 2.45
Step-by-step Solution
Detailed explanation
The sum of all probabilities in a probability distribution is always unity.
\(\therefore \mathrm{k}+0.3 +0.15+0.15+0.1+2 \mathrm{k}=1 \)
\( \Rightarrow 3 \mathrm{k} \)
\( \Rightarrow +0.7=1 \)
\( \Rightarrow 3 \mathrm{k} =0.3 \)
\(\Rightarrow \mathrm{k} =0.1 \)
\( \therefore \mathrm{E}(\mathrm{X}) =\sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right) \)
\( =0(0.1)+1(0.3)+2(0.15)+3(0.15) \)
\( =0.3+0.3+0.45+0.4+1 \)
\( =2.45 \)
\(\therefore \mathrm{k}+0.3 +0.15+0.15+0.1+2 \mathrm{k}=1 \)
\( \Rightarrow 3 \mathrm{k} \)
\( \Rightarrow +0.7=1 \)
\( \Rightarrow 3 \mathrm{k} =0.3 \)
\(\Rightarrow \mathrm{k} =0.1 \)
\( \therefore \mathrm{E}(\mathrm{X}) =\sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right) \)
\( =0(0.1)+1(0.3)+2(0.15)+3(0.15) \)
\( =0.3+0.3+0.45+0.4+1 \)
\( =2.45 \)
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