Suppose the random variable x comes from a distribution with mean 5 and standard deviation 3. a). If L = 6 + 2x, what is the L? b). What is L? Solution Given mean=5, s=3 (a) mean(L) = mean(6+2x) = 6+2*mean(x) = 6+2*5=16 (b) s(L)= s(6+2x) = 2*s(x)=2*3=6.

1. suppose the random variable X has a geometric distribution with P=0.3 .Determine the following
probabilities:
P(X=1)
P(X>=1)
P(X=3)
P(X<3)
Solution
((1-p)^(k-1) )*P
a)
=0.7^0 *0.3=0.3
b)

2. 1-0.3=0.7
c)
(0.7)^2 *0.3=0.147
d)
1-0.147=0.853