A random variable has the following probability distribution: P(X = xi) = 0, 2p, 2p, 3p, p^2, 2p^2

Question

A random variable has the following probability distribution:

X = xi:	0	1	2	3	4	5	6	7
P(X = xi):	0	2p	2p	3p	p2	2p2	7p2	2p

The value of p is

A. 1/10

B. –1

C. – 1/10

D. 1/5

Answer 1

Correct answer is A.

The probability distribution of X is:

We Know that

Therefore,

⇒ 2p + 2p + 3p + p² + 2p² + 7p² + 2p = 1

⇒ 10p² + 9p - 1 = 0

⇒ 10p² + 10p - p -1 = 0

⇒ 10p(p + 1) -1(p + 1) = 0

⇒ (10p - 1)(p + 1)

10p - 1 = 0 or p + 1 = 0

p = \(\frac{1}{10}\) or p = -1

We considered  p = \(\frac{1}{10}\) because p is a probability and probability cannot be in negative

Option (B) is incorrect because p is a probability and probability cannot be in negative

Option (C) is incorrect because p is a probability and probability cannot be in negative

Option (D) is incorrect because by putting p = \(\frac{1}{5},\) the sum total of pxi is not equal to 1