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Question
A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X = 3) = 2 P (X = 1) and P (X = 2) = 0.3, then P (X = 0) is
Options
0.1
0.2
0.3
0.4
Solution
0.4
Let:
P(X = 0) = m
P(X = 1) = k.
Now,
P(X = 3) = 2k
| xi | pi | pixi |
| 0 | m | 0 |
| 1 | k | k |
| 2 | 0.3 | 0.6 |
| 3 | 2k | 6k |
Mean = \[\sum\nolimits_{}^{}\] pixi
\[0 + k + 0 . 6 + 6k = 1 . 3\]
\[ \Rightarrow 7k = 1 . 3 - 0 . 6\]
\[ \Rightarrow k = \frac{0 . 7}{7} = 0 . 1\]
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1
\[\Rightarrow m + 0 . 1 + 0 . 3 + 0 . 2 = 1\]
\[ \Rightarrow m + 0 . 6 = 1\]
\[ \Rightarrow m = 0 . 4\]
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