1. Continuous Distributions
Uniform distribution.
Exponential distribution.
By one convention, a random variable X is
called continuous if its cumulative distribution
function is continuous.
Ex.
Shashwat Shriparv
dwivedishashwat@gmail.com
InfinitySoft

2. Uniform distribution …..
 A random variable X is uniformly
distributed on the interval interval (a,b) if
its pdf is given by
 The cdf is

3. pdf and cdf of Uniform distribution
Probability density function Cumulative distribution function

4.  E(X)=(a+b)/2
 V(X)=(b-a)2/12

5. Example
 A bus arrives every 20 miutes at a
specified stop beginning at 6:40 AM
and continuing until 8:40 am. A
certain passenger does not know
the schedule, but arrives randomly
(uniformly distributed) between
7:00 am and 7:30 am every
morning. What is the probability
that the passenger waits more than
minutes for a bus?

6. Exponential distribution
 A random variable X is said to be
exponentially distributed with parameter
λ > 0 if its pdf is given by

7. Probability density function

8. Cumulative distribution function

9. Exponential distribution ….

10. Example
 suppose that the life of an industrial
lamp, in thousands of hours , it
exponentially distributed with failure
rate λ=1/3 (one of failure every 3000 hours,
on average).. The probability that the lamp
will last longer than its mean life of giving
3000 hours is given by P(X>3)=1-P(X<=3) =
1-F(3)
 P(X>3)=1-(1-e-3/3)=e-1 =0.368
Shashwat Shriparv
dwivedishashwat@gmail.com
InfinitySoft