1. Define random variables.
variable, usually written X, is a variable whose possible values are numerical
outcomes of a random phenomenon. Random variable consists of two types they are
discrete and continuous type variables.
2. What is meant by probability distribution?
probability distribution of a discrete random variable is a list of
probabilities associated with each of its possible values. It is also sometimes
called the probability function or the probability mass function.
3. What are the conditions applied in the central
 The mean
of the population of means is always equal to the mean of the parent population
from which the population samples were drawn.
standard deviation of the population of means is always equal to the standard
deviation of the parent population divided by the square root of the sample
distribution of means will increasingly approximate a normal distribution as
the size N of samples increases.
process is a stochastic process whose joint probability distribution does not
change when shifted in time. Consequently, parameters such as the mean and
variance, if they are present, also do not change over time and do not follow
5.Write the equation for correlation?
population correlation coefficient ρX,Y between two random variables X and Y
with expected values μX and μY and standard deviations σX and σY is defined as:
6. what is meant by covariance?
is a measure of how much two variables change together, and the covariance
function, or kernel, describes the spatial covariance of a random variable
process or field.
7. Define random process.
process X(t) is a Gaussian process if for all n and all (t1 ,t2 ,…,tn ), the
random variables have a jointly Gaussian density function.
8. Write the equation of Autocorrelation?
autocorrelation function of the output random process Y (t). By definition, we
RY (t, u)
= E[Y (t)Y (u)]
and u denote the time instants at which the process is observe
9.Write the applications of random process?
available noise power is directly proportional to temperature and it is
independent of value of resistance. This power specified in terms of
temperature is called as noise temperature. It is denoted by Te . It is given
• Te =(F−1)T A Gaussian process can be used as
a prior probability distribution over functions in Bayesian inference.
process (aka Brownian motion) is the integral of a white noise Gaussian
process. It is not stationary, but it has stationary increments.