## Question

###### 3. (15 points) For the following cumulative mass function 01 10.3 0. (a) Derive the mass...

3. (15 points) For the following cumulative mass function 01 10.3 0. (a) Derive the mass funciton, (b) Find the probability that P ( 3) II) P (3 <x 36) HI) P(x26)

## Answers

a)

x f(x) 1 F(1) = 0.1 2 F(2) - F(1) = 0.3 - 0.1 = 0.2 3 F(3) - F(2) = 0.3 - 0.3 = 0 4 F(4) - F(3) = 0.4 - 0.3 = 0.1 5 F(5) - F(4) = 0.8 - 0.4 = 0.4 6 F(6) - F(5) = 0.9 - 0.8 = 0.1 7 F(7) - F(6) = 1 - 0.9 = 0.1 b) i) P(X = 3) = 0

ii) P(3 < X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1 + 0.4 + 0.1 = 0.6

iii) P(X > 6) = P(X = 6) + P(X = 7) = 0.1 + 0.1 = 0.2

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