An unbiased die is rolled. If the random variable $\mathrm{X}$ is defined as,
$X= \begin{cases}1 & \text { if the outcome is a number less than or equal to } 3 \\ 0 & \text { if the outcome is a number greater than } 3\end{cases}$
Then the probability distribution of X is :
Answer & explanation
Correct answer: option 3
$x= \begin{cases}1 & \text { outcome } \leq 3 \\ 0 & \text { outcome }>3\end{cases}$
Total outcomes of a die = 6
for x = 1 (outcomes $\leq$ 3) → no of favourable cases = 3
(since 1, 2, 3 are less than or equal to 3)
for x = 0 (outcomes > 3) → no of favourable cases = 3
(since 4, 5, 6 are greater than or equal to 3)
|
For |
x = 0 |
x = 1 |
|
|
$~P(x)=\frac{3}{6}=\frac{1}{2}~~$ |
$~~P(x)=\frac{3}{6}=\frac{1}{2}~$ |
probability distribution
|
X |
0 |
1 |
|
P(X) |
1/2 |
1/2 |