# Question

The number of defects in a machine-made product is a random variable X with the following probability distribution:

X P(x)

0 ..... 0.1

1 ..... 0.2

2 ..... 0.3

3 ..... 0.3

4 ..... 0.1

a. Show that P(x) is a probability distribution.

b. Find the probability P(1 < X ≤ 3).

c. Find the probability P(1 < X ≤ 4).

d. Find F(x).

X P(x)

0 ..... 0.1

1 ..... 0.2

2 ..... 0.3

3 ..... 0.3

4 ..... 0.1

a. Show that P(x) is a probability distribution.

b. Find the probability P(1 < X ≤ 3).

c. Find the probability P(1 < X ≤ 4).

d. Find F(x).

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