Give the mean , , variance , 2, and standard deviation , , of the sum X + Y in e
ID: 2930495 • Letter: G
Question
Give the mean , , variance , 2, and standard deviation , , of the sum X + Y in each of the following cases. (Round the answers for to the nearest thousandths.)
(a) X is a binomial random variable with n = 20, p = 0.6. Y is a binomial random variable with n = 10, p = 0.4. X and Y are independent.
=
^2 =
=
What distribution does the sum have, normal or binomial?
Normal.
Binomial.
The name of the exact distribution cannot be given.
(b) X is a normal random variable with = 100 and = 14. Y is a normal random variable with = 50 and = 8. X and Y are independent.
=
^2 =
=
What distribution does the sum have, normal or binomial?
Normal.
Binomial.
The name of the exact distribution cannot be given.
(c) X is a normal random variable with = 50 and = 18. Y is a binomial random variable with n = 100, p = 0.28. X and Y are independent.
=
^2 =
=
What distribution does the sum have, normal or binomial?
Normal.
Binomial.
The name of the exact distribution cannot be given.
Explanation / Answer
a)
b)
normal
c)
mean = E(X+Y)= E(X)+E(Y)
= 50 + np = 50 +100 *0.28 = 78
variance = Var(X+Y) = Var(X) +Var(Y)
= 18^2 + 100*0.28*(1-0.28)
= 344.16
sd = sqrt(344.16)
= 18.5515
The name of the exact distribution cannot be given.
x y n 20 10 p 0.6 0.4 mean 16 variance 7.2 sd 2.6832816Related Questions
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