Question

Define uniform distribution, find mean and variance. Also find the exponential distribution using the uniform distribution.​

Answer 1

Answer:

Let X have a uniform distribution on (a,b) . The density function of X is

f(x)=1b−a if a≤x≤b and 0 elsewhere

The the mean is given by

E[X]=∫baxb−adx=b2−a22(b−a)=b+a2

The variance is given by E[X2]−(E[X])2

E[X2]=∫bax2b−adx=b3−a33(b−a)=b2+ba+a23

The required variance is then

b2+ba+a23−(b+a)24=(b−a)212