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Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 are
  • a)
    0 and 0.5
  • b)
    0.5 and 1
  • c)
    0 and 1
  • d)
    0.25 and 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a random variable x that takes values +1 and -1 with probabil...
The PDF of the random variable is

The cumulative distribution function F(x) is the probability upto x as given below
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Most Upvoted Answer
Consider a random variable x that takes values +1 and -1 with probabil...
Cumulative Distribution Function (CDF)

The cumulative distribution function (CDF) of a random variable gives the probability that the random variable takes on a value less than or equal to a given value. In other words, it gives the cumulative probability distribution of the random variable.

Given Information

The given random variable x takes values 1 and -1 with probability 0.5 each. This means that the probability of x being equal to 1 is 0.5, and the probability of x being equal to -1 is also 0.5.

Determining the CDF at x = -1 and x = 1

To determine the CDF at x = -1 and x = 1, we need to calculate the cumulative probabilities.

At x = -1:
The cumulative probability at x = -1 is the probability that x takes on a value less than or equal to -1. Since the only possible value of x that is less than or equal to -1 is -1 itself, the cumulative probability at x = -1 is equal to the probability of x being -1. In this case, the probability of x being -1 is 0.5. Therefore, the CDF at x = -1 is 0.5.

At x = 1:
Similarly, the cumulative probability at x = 1 is the probability that x takes on a value less than or equal to 1. Since the only possible value of x that is less than or equal to 1 is 1 itself, the cumulative probability at x = 1 is equal to the probability of x being 1. In this case, the probability of x being 1 is also 0.5. Therefore, the CDF at x = 1 is 0.5.

Final Answer

The value of the cumulative distribution function F(x) at x = -1 is 0.5, and at x = 1 is also 0.5. Therefore, the correct answer is option 'C' - 0 and 1.
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Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0.5 and 1c)0 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer?
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