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Consider a random variable Xthat 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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a random variable Xthat takes values +1 and -1 with probabili...
The p.d.t of the random variable is

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

The cumulative distribution function (CDF) of a random variable X is a function that gives the probability that X will take on a value less than or equal to x. It is denoted by F(x).

Given Information:

In this problem, we are given a random variable X that takes values 1 and -1 with equal probabilities of 0.5 each. We need to find the values of the cumulative distribution function (CDF) at x = -1 and x = 1.

Solution:

To find the CDF, we need to calculate the cumulative probabilities for each value of X.

Cumulative Probability for X = -1:

The cumulative probability for X = -1 is the sum of the probabilities of all values of X less than or equal to -1.

Since X can only take on the values 1 and -1, the cumulative probability for X = -1 is equal to the probability of X = -1.

P(X ≤ -1) = P(X = -1) = 0.5

Hence, the value of the CDF at x = -1 is 0.5.

Cumulative Probability for X = 1:

Similarly, the cumulative probability for X = 1 is the sum of the probabilities of all values of X less than or equal to 1.

Since X can only take on the values 1 and -1, the cumulative probability for X = 1 is equal to the sum of the probabilities of X = -1 and X = 1.

P(X ≤ 1) = P(X = -1) + P(X = 1) = 0.5 + 0.5 = 1

Hence, the value of the CDF at x = 1 is 1.

Summary:

The values of the cumulative distribution function (CDF) at x = -1 and x = 1 are 0.5 and 1, respectively.

Therefore, the correct answer is option C: 0.5 and 1.
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Consider a random variable Xthat takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer?
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Consider a random variable Xthat takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a random variable Xthat takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a random variable Xthat takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer?.
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