(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.
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.
(2 points) Consider a random variable X that takes the values 0, 50, 100, 150, and...
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