The distribution function of a random variable is given by
F(x)= {0 , for x<-1
{(x+1)/2 , for -1<x<1
{1 , for x≥1.
Find P(3<x<4)
To find P(3 < x < 4), we need to evaluate the cumulative distribution function (CDF) at both endpoints and then subtract the CDF values to get the probability of the given interval.
The given distribution function is:
F(x) = {
0, for x < -1,
(x+1)/2, for -1 < x < 1,
1, for x ≥ 1
}
To find P(3 < x < 4), we can evaluate the CDF at x = 4 and x = 3 and then subtract the CDF values.
First, let's evaluate the CDF at x = 4:
F(4) = 1, since 4 ≥ 1.
Next, let's evaluate the CDF at x = 3:
F(3) = (3+1)/2 = 2/2 = 1.
Now, we can subtract the CDF values:
P(3 < x < 4) = F(4) - F(3) = 1 - 1 = 0.
Therefore, the probability P(3 < x < 4) is 0.