Since the cumulative distribution function is defined as F(x) = P(X ≤ x), we can find the probability of each value of X by plugging in the values of x into the given function.
For x = 1:
F(1) = P(X ≤ 1) = 1 + A
Since X can only take on the values {1,2,3}, the probability that X = 1 is equal to F(1), which means P(X = 1) = 1 + A.
For x = 2:
F(2) = P(X ≤ 2) = 2 + A
Similarly, the probability that X = 2 is equal to F(2), so P(X = 2) = 2 + A.
For x = 3:
F(3) = P(X ≤ 3) = 3 + A
This means that P(X = 3) = F(3) = 3 + A.
Since the sum of the probabilities of all possible values of a discrete random variable must equal 1, we have:
P(X = 1) + P(X = 2) + P(X = 3) = (1 + A) + (2 + A) + (3 + A) = 1
6 + 3A = 1
3A = -5
A = -5/3
Therefore, the value of A is -5/3.
The discrete random variable X
has a cumulative distribution function, F(x)=P(X≤x)
, defined by
F(x)=(x+A8)
, x=1,2,3
Note: Range of X={1,2,3}
Find the value of A
.
1 answer