Question

The distribution function F(X) of discrete random variable X is given by

X	1	2	3	4	5	6
F (X = x)	0.2	0.37	0.48	0.62	0.85	1

Then P [X = 4] + P [X = 5] =

• A. 0.14
• B. 0.85
• C. 0.37
• D. 0.23

Answer 1

Answer: (C)

0.37

Answer 2

The probability mass function (pmf) is obtained from the cumulative distribution function (cdf) by differences:

$$P(X=x) = F(x) - F(x^-)$$

• $P(X=4) = F(4) - F(3) = 0.62 - 0.48 = 0.14$
• $P(X=5) = F(5) - F(4) = 0.85 - 0.62 = 0.23$

So,

$$P(X=4) + P(X=5) = 0.14 + 0.23 = 0.37$$