GATE DA 2024 Set 1 — Question 11
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Probability & Statistics → Continuous Random Variables → Poisson
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Question
Consider the following statements:(i) The mean and variance of a Poisson random variable are equal.
(ii) For a standard normal random variable, the mean is zero and the variance is one.Which ONE of the following options is correct?
(ii) For a standard normal random variable, the mean is zero and the variance is one.Which ONE of the following options is correct?
Correct answer
(A) Both (i) and (ii) are true
Solution
Statement (i) is true: For a Poisson distribution with parameter , both the mean and the variance are equal to .
Statement (ii) is true: By definition, a standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.
Therefore, both statements are true.
Statement (ii) is true: By definition, a standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.
Therefore, both statements are true.
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