Question

A random variable X has the following has the following:

X = x	–2	–1	0	1	2	3	4
P(X = x)	6k	8k	5k	4k	6k	11k	7k

Then, the value of P(–1 < X < 3) is ______.

Options

• `26/49`

• `15/47`

• `23/49`

• `34/49`

Answer 1

A random variable X has the following has the following:

X = x	–2	–1	0	1	2	3	4
P(X = x)	6k	8k	5k	4k	6k	11k	7k

Then, the value of P(–1 < X < 3) is `15/47`.

Explanation:

Since `sum_(x = -2)^4 "P"("X" = x)` = 1,

6k + 8k + 5k + 4k + 6k + 11k + 7k = 1

⇒ 47k = 1

⇒ k = `1/47`

∴ P(–1 < X < 3) = P(X  0 + P(X = 1) + P(X = 2)

= 5k + 4k + 6k

= 15k

= `15/47`