which are both Gaussian (or normal) distributed with zero mean and variance
. Determine
the probability density function of 
.
H. (20%) Consider a continuous random variable X.X is said
to be memoryless if Pr{X>t+h|X>t}=Pr{X>h} for constants h and
t . Please show that X is memoryless if and only if X is exponentially
distributed.
(20%) Let V=
,where
x denotes the variable and R is the set consisting of all real numbers.
Define the inner product of functions f(x)and g(x)
,where
x denotes the variable and R is the set consisting of all real numbers.
Define the inner product of functions f(x)and g(x)
(8%)(b) Are X and Y independent? Why?
V
forms a vector space over the field consisting of all complex numbers, and
is a basis
for V, where Z+ denotes the set containing all positive integers.
Please show that 
also
forms a basis for V, where Z stands for the set containing all integers.
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