1. Find , , if a random variable is given by its density function , such that
, if
, if 0 <
, if > 1
2. Let be given by its distribution function , such that
if
, if 0 <
, if > 2
a) Graph the distribution function
b) Graph the density function
c) Find , ,
3. A random variable is distributed normally with and . Find p(3?X<4.5).
4. The distribution of daily requests to a certification authority for public-key certificates is normal with the expectation of 100 and the standard deviation of 15.
a) Find the probability that the number of requests on Monday is between 95 and 105.
b) Find the probability that the number of requests on Tuesday is greater than 120.
c) Find the probability that the number of requests on Wednesday is less than 121.
5. The density function of a random variable is given by
Find its (a) math expectation, (b) variance and (c) distribution function.
Find the density function of a normally distributed random variable , if and
It’s known that a random variable is distributed normally with and it’s also known that