The probability distribution of a random variable X is given by:
| X | 0 | 1 | 2 |
|---|---|---|---|
| P(X) | k | 2k | 3k |
In any probability distribution, all probabilities must sum to 1.
P(X=0)+P(X=1)+P(X=2)=1
k+2k+3k=1
6k=1
k=61
The expression P(0<X≤2) represents the probability that X is greater than 0 and less than or equal to 2.
From the table, this includes X = 1 and X = 2, but excludes X = 0.
P(0<X≤2)=P(X=1)+P(X=2)
P(0<X≤2)=2k+3k
P(0<X≤2)=5k
P(0<X≤2)=5×61
P(0<X≤2)=65