The probability distribution of a random discrete variable is given
| X | -1 | 0 | 1 | 2 | 3 |
| P(X) | 0.1 | p | 0.3 | q | r |
If it is known that P(X=1) is the mean of P(X=0) and P(X=2).
Then the value of \(r\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
P(X = 1) is the mean of P(X = 0) and P(X = 2):
\( \displaystyle 0.3 = \frac{p + q}{2} \)
\(p + q = 0.6\)
The probabilities add up to 1:
\(0.1 + p + 0.3 + q + r = 1\)
\(0.4 + 0.6 + r = 1\)
\(r = 0\)