Question

Verify whether the following function is a cumulative distribution function of a random variable Y. Consider all three properties of CDF and show explicitly which properties are satisfied and which are not satisfied.
F(y)=0.1 if y<1
0.3 if 1<=y<5
0.4 if y=5
1 if y>5

Answer 1

was the last one correct?

Answer 2

yep

Answer 3

can you list the three properties?

Answer 4

lets call the cumulative function F(x). it has three properties
1. F(x) is non decreasing
2. lim F(x) as x->-00 = 0
3. lim F(x) as x->+oo = 1
so your function satisfies properties 1 and 3, but not property 2

Answer 5

does that make sense?

Answer 6

you need y value to be zero