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?
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 ? for Y.
(ii).Let 
. Then 
, which is less than 3 because 1 - p < 1. Now let Y have a Poisson distribution with mean 3. The variance of Y is also equal to 3, because the variance of a Poisson random variable is always equal to its mean. Therefore Y has a larger variance than X.
You might also like to view...
Joint sealants that have excellent flexibility and elongation properties are classified as _____.
a. polymeric b. thermoplastic c. elastomeric d. hydrostatic
Rikardo sold his calves averaging 589 pounds. How many kilograms did they average?
What will be an ideal response?
Mechanical digestion in birds occurs in the mouth, just as it does in mammals.
Answer the following statement true (T) or false (F)
A company carries an average annual inventory of $1,000,000. If the cost of capital is 10%, storage costs are 8%, and risk costs are 7%, what does it cost per year to carry this inventory?
A) $70,000 B) $250,000 C) $100,000 D) $80,000 E) cannot be determined from the data given