Question

A random variable X has following probability distribution

X = x	1	2	3	4	5	6
P(X = x)	K	3K	5K	7K	8K	K

Then P(2 ≤ X < 5) = _____.

Options

• `3/5`

• `7/25`

• `23/25`

• `24/25`

Answer 1

`3/5`

Explanation:

We know that, ∑ pi = 1

⇒ k + 3k + 5k + 7k + 8k + k = 1

⇒ 25k = 1

⇒ k = `1/25`

Now, P(2 ≤ X < 5)

= P(X = 2) + P(X = 3) + P(X = 4)

= 3k + 5k + 7k = 15k

= `15 xx 1/25 = 3/5`