The distribution of daily requests to a certification authority for public-key certificates

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 

6. It’s known that a random variable  is distributed normally with  and it’s also known that < < Find < .