Consider a random variable \(X\) that takes values +1 and −1 with probability…
2012
Consider a random variable \(X\) that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function \(F(x)\) at \(x\) = −1 and +1 are
- A.
0 and 0.5
- B.
0 and 1
- C.
0.5 and 1
- D.
0.25 and 0.75
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Correct answer: C
Compute the cumulative distribution function F(x) = P(X ≤ x).
At x = -1: F(-1) = P(X ≤ -1) = P(X = -1) = 0.5.
At x = 1: F(1) = P(X ≤ 1) = P(X = -1 or X = 1) = 1.
Therefore the values of the cumulative distribution function at x = -1 and x = 1 are 0.5 and 1, respectively.