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σ2i. Show that Y= ΣnI=1 αi Xi, where the αi are scalars, is normally distributed, and find its
mean and variance. Use moment generating functions to show. 2 [STAT 100A/SANCHEZ TA SESSION] 7
Practicing discrete bivariate distributions
5. Suppose that 15 percent of the families in a certain community have no children, 20
percent have 1, 35 percent have 2, and 30 percent have 3; and suppose, further, that in
each family, each child is equally likely (independently) to be a boy or a girl. If a family
is chosen at random from this community, then B, the number of boys, and G, the number
of girls, in this family will have the joint probability mass function shown below.
Table 6.2 in Ross, p. 261 P(B=i, G=j)
G=0
G=1
G=2
G=3
B=0
0.15
0.1
0.0875
0.0375
B=1
0.1
0.175
0.1125
0
B=2
0.0875
0.1125
0
0
B=3
0.0375...
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This note was uploaded on 03/04/2014 for the course STAT 100A taught by Professor Wu during the Winter '10 term at UCLA.
 Winter '10
 Wu

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