Question

The probability distribution of X is 

X = x	-4	-3	-2	-1	0	1	2
P(X = x)	0.25a	0.20a	0.15a	0.10a	0.05a	0.10a	0.15a

Then P(X is not a natural number) = ______ 

Options

• 0.45

• 0.55

• 0.65

• 0.75

Answer 1

0.75

Explanation:

SInce `sum_{x = -4}^2`P(X = x) = 1,

0.25a + 0.20a + 0.15a + 0.10a + 0.05a + 0.10a + 0.15a = 1 

⇒ a = 1

P(X is not a natural number)

= P(X = -4) + P(X = -3) + P(X = -2) + P(X = -1) + P(X = 0)

= 0.25 + 0.20 + 0.15 + 0.10 + 0.05 = 0.75