Multiple choice

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

  1. 0 and 0.5

  2. 0 and 1

  3. 0.5 and 1

  4. 0.25 and 0.75
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C Correct answer
Explanation

The cumulative distribution function F(x) = P(X $\le$  x) F(-1) = P(X $\le$ -1) = P(X = -1) = 0.5 F(+1) = P(X $\le$ +1) = P(X = -1)+P(x  =  + 1) = 0.5 + 0.5 = 1

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