Question

Suppose a certain character in a role-playing game has an ability to use in battles. When activated, the ability deals damage to an enemy using X hits, where X is a random variable with the following cumulative distribution function The chance of getting between 2 and 4 hits is 0.46 . The chance of getting exactly 3 hits is

Answer 1

The chance of getting exactly 3 hits is = 0.20

Explanation:

P.S - The exact question is -

As given,

F(x) = 0 , x < 1

0.30 , 1 ≤ x < 2

0.56 , 2 ≤ x < 3

0.76 , 3 ≤ x < 4

0.9 , 4 ≤ x < 5

1 , 5 ≤ x

Now,

f(x) = 0.30 , x = 1

0.56 - 0.30 = 0.26 , x = 2

0.76 - 0.56 = 0.20 , x=3

0.9 - 0.76 = 0.14 , x = 4

1 - 0.9 = 0.1 , x = 5

0, otherwise

Now,

The chance of getting exactly 3 hits is = f(x = 3) = 0.20