A random variable X has the following probability distribution
|
X |
0 |
1 |
2 |
3 |
4 |
5 |
|
P(X) |
0.1 |
k |
0.2 |
2k |
0.3 |
k |
Then $P (X < 3)$ is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.4
Given:
$P(X=0) = 0.1$, $P(X=1) = k$, $P(X=2) = 0.2$, $P(X=3) = 2k$, $P(X=4) = 0.3$, $P(X=5) = k$
Total probability must sum to 1:
$0.1 + k + 0.2 + 2k + 0.3 + k = 1$
$0.6 + 4k = 1$
$4k = 0.4 \Rightarrow k = 0.1$
Now, compute $P(X < 3) = P(X=0) + P(X=1) + P(X=2)$
$= 0.1 + k + 0.2 = 0.1 + 0.1 + 0.2 = {0.4}$