Question

(2 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X − 100| be the (absolute) deviation of X from its average value 100. Compute the probability mass function (PMF) and cumulative distribution function (CDF) of Y . Explain.

Answer 1

here from above pmf of X:

x	f(x)
0	0.2
50	0.2
100	0.2
150	0.2
200	0.2

therefore from above pmf of Y:

Y=|X-100|	f(y)
100	0.2
50	0.2
0	0.2
50	0.2
100	0.2

adding probability of duplicate values of y ; final pmnf of Y:

Y	f(y)
0	0.2
50	0.4
100	0.4

from given pmf below id CDF F(y) of Y:

range (Y)	F(y)
y<0	0
0<=y<50	0.2
50<=y<100	0.6
y>=100	1

please revert for any clarification.