When x has a binomial distribution with total number n of trials and success probability p ,we use the notation, X ~ B(n, p) . Suppose that independent random variables x and y have binomial distributions such that X ~ B(n, p) and Y ~ B(n, q) ,where 0

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Chapter1: Combinatorial Analysis
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of trials and success probability p ,we use the notation, X ~
~ B(n, p)
When x has a binomial distribution with total number n
Suppose that independent random variables x and y have binomial distributions such that X ~
B(n, p) and Y B(n, q) ,where
0 < p<1_and 0<q<1•
Answer the following true/false questions.
The mgf of X +Y is 2(pe + (1 – p))" when p=q
Choose... +
X(1 – Y) ~ B(1, p(1 – q)) when
n = 1
Choose... +
(n – X +Y) ~ B(2n, q) when p+q = 1
Choose... +
P(X = x, Y = y) = P(XY = xy)
Choose... +
E[X +Y] =
= 2n when
p+q=1
Choose... +
| (n – X) ~ B(n,1 p)
Choose... +
Transcribed Image Text:of trials and success probability p ,we use the notation, X ~ ~ B(n, p) When x has a binomial distribution with total number n Suppose that independent random variables x and y have binomial distributions such that X ~ B(n, p) and Y B(n, q) ,where 0 < p<1_and 0<q<1• Answer the following true/false questions. The mgf of X +Y is 2(pe + (1 – p))" when p=q Choose... + X(1 – Y) ~ B(1, p(1 – q)) when n = 1 Choose... + (n – X +Y) ~ B(2n, q) when p+q = 1 Choose... + P(X = x, Y = y) = P(XY = xy) Choose... + E[X +Y] = = 2n when p+q=1 Choose... + | (n – X) ~ B(n,1 p) Choose... +
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