Question

The following is the c.d. f. of a discrete r.v. X. Find : (i) the p.m.f. of X, (ii) P(-1 ≤ X < 2), (iii) P(X ≥ 5). (iv) P (X = -3|X < 0), (v) P(X ≤ 3|X > 0).
X = x:
-3
-1
0
1
3
5
7
9

F (x):
0.1
0.3
0.5
0.65
0.75
0.85
0.90
1

Answer 1

Answer:

Step-by-step explanation:

x:           F(x)         P(x)

-3           0.1          0.1

-1           0.3          0.2

0           0.5          0.2

1           0.65          0.15

3           0.75          0.1

5           0.85          0.1

7           0.90         0.05

9           1                0.1

P(-1 ≤ X < 2) = P(-1) + P(0) + P (1) = 0.2 + 0.2 + 0.15 = 0.55

P(X ≥ 5) = P(5) + p(7) + P(9) = 0.1 +0.05 + 0.1  = 0.25