Exercise 11.3: Continuous Distributions

EXERCISE 11.3

1. The probability density function of X is given by 

Find the value of k .

2. The probability density function of X is 

Find (i) P (0.2 ≤ X < 0.6) (ii) P (1.2 ≤ X < 1.8) (iii) P (0.5 ≤ X < 1.5)

3. Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function

Find (i) the value of k (ii) the distribution function (iii) the probability that daily sales will fall between 300 litres and 500 litres?

4. The probability density function of X is given by 

Find (i) the value of k (ii) the distribution function (iii) P(X < 3) (iv) P (5 ≤ X ) (v) P(X ≤ 4).

5. If X is the random variable with probability density function f ( x) given by,

then find (i) the distribution function F ( x) (ii) P ( −0.5 ≤ X ≤ 0.5)

6. If X is the random variable with distribution function F ( x) given by,

then find (i) the probability density function f ( x) (ii) P ( 0 .3 ≤ X ≤ 0 .6)

Answers:

(1) 4

(2) (i) 0.16 (ii) 0.3 (iii) 0.75