Consider the following statements: (i) The mean and variance of a Poisson…
2024
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?
- A.
Both (i) and (ii) are true
- B.
(i) is true and (ii) is false
- C.
(ii) is true and (i) is false
- D.
Both (i) and (ii) are false
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Answer: Both statements are true.
(i) For a Poisson distribution with parameter λ: the mean and variance are both equal to λ. This is a standard property of the Poisson distribution: if X ~ Poisson(λ), then E[X] = λ and Var(X) = λ.
(ii) The standard normal distribution is defined as the normal distribution with mean 0 and variance 1. If Z denotes a standard normal random variable, then E[Z] = 0 and Var(Z) = 1.
Therefore, both given statements are true.