STAT/MATH 394B

Solutions, homework 7

3.2.4

3.2.5 f(x) = (d/dx)F(x) = 9x²-8x, 0 <=x < 1; 0 otherwise

3.2.10

Note that the book answer had a typo in it.

3.3.5 (a) P(X=3) =9/14

(b) P(X<=2.7614)=P(X<=2)=1-P(X=3)=5/14 (from (a))

(c) P(X=2.7614)=0; not a possible value for X

(d) P(X<=2)=5/14 from (b)

(e)P(X<2)=P(X=1)=1/14

3.3.6 X ~ Bin(3,1/6) so P(X=k) = .

or P(X=0)=(5/6)³=125/216; P(X=1)=3(1/6)(5/6)²=75/216; P(X=2)=3(1/6)²(5/6)=15/216; P(X=3)=(1/6)³=1/216

3.3.11 (a)

(b)