(i)
F(x) changes value at x = - 3, -1, 1, 3, 5, 7
So,
Range of X is given by:
{-3, -1, 1, 3, 5, 7}
So,
f(-3) = 0.1
f(-1) = F(-1) - F(-3) = 03 - 0.1 = 0.2
f(1) =F(1) - F(-1) = 0.6 - 0.3 = 0.3
f(3) = F(3) - F(1) = 0.8 - 0.6 = 0.2
f(5) = F(5) - F(3) = 0.9 - 0.8 = 0.1
f(7) = F(7) - F(5) = 1.0 - 0.9 = 0.1
Thus,
the probability distribution of x is given by:
X | f(X) |
- 3 | 0.1 |
- 1 | 0.2 |
1 | 0.3 |
3 | 0.2 |
5 | 0.1 |
7 | 0.1 |
(ii)
P(X<1) = f(-1) + f(-3) = 0.2 + 0.1 = 0.3
(iii)
P(0<X5) = f(1) + f(3) + f(5) = 0.3 + 0.2 + 0.1 = 0.6
Consider the following cumulative distribution function for X. 7 0.1 08 0.9 1.0 Fo) 0.3 0.6...
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