Question

If a discrete random variable X follows uniform distribution and assume only the values 8, 9, 11, 15, 18, 20, the value of P(|X - 14| < 5) will be:
1. \(\dfrac{1}{5}\)
2. \(\dfrac{1}{4}\)
3. \(\dfrac{1}{3}\)
4. \(\dfrac{1}{2}\)

Answer 1

Correct Answer - Option 4 : \(\dfrac{1}{2}\)

Given

In discrete random variable X follows uniform distribution

Assumed values of X = 5. 9, 11, 15, 18, 20

Calculation

I X – 14 I < 5

⇒ - 5 <  X – 14 < 5

⇒ 9 < X <, 19

∴ Favourable case = {11, 15, 18} = 3

Total sample space = {8, 9, 11, 15, 18, 20} = 6

⇒ P(IX – 14I < 5) = P(9 < X < 19)

⇒ Favourable case/total sample space = 3/6

∴ The value of P(IX – 14I < 5 is ½