Assignment – Module 1
1. Check whether the function
( )
( )
2
31
4
x
fx −
=
-1 < x < 1
= 0 elsewhere
is a probability density function (pdf). If the function is a pdf, obtain P[0.25 < X < 0.5]
2. The pdf of a random variable X is given as
f(x) = ce-2x x > 0
i. Obtain the value of ‘c’,
ii. Obtain the CDF
iii. Obtain the value of x if P[X < x] = 0.5
3. The joint pdf of two random variables X and Y is given as
f(x,y) = c(2x+y) 0 < x < 1, 0 < y < 1
= 0 elsewhere
Obtain the constant ‘c’ and obtain P[X > 0.5, Y > 0.5]
4. Obtain the marginal density function of X and the marginal density function of Y for the
joint pdf in problem no.3.
Also obtain P[X > 0.5]*P[Y > 0.5]. Is this probability the same as P[X > 0.5, Y > 0.5]?
Explain the reason.
5. The joint pdf of two random variables X and Y is given as
f(x,y) = cxy 0 < x < 1, 1 < y < 2
= 0 elsewhere
i. Obtain the value of ‘c’,
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