A random variable \(X\) has a binomial distribution, and a random variable \(Y\) has a Poisson distribution. Both \(X\) and \(Y\) have means equal to 3. Is it possible to determine which random variable has the larger variance? Choose one of the following answers:

i. Yes, \(X\) has the larger variance.

ii. Yes, \(Y\) has the larger variance.

iii. No, we need to know the number of trials, \(n\), for \(X\).

iv. No, we need to know the success probability, \(p\), for\(X\).

v. No, we need to know the value of \(\lambda\) for \(Y\) .

Equation Transcription:

Text Transcription:

X

Y

n

p

lambda

Solution

Step 1 of 2

Here XB(n,p)

The mean of the binomial distribution is ‘np’=3

The variance of the binomial distribution is ‘np(1-p)’<3

Because 1-p<0