Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 Iitres and a maximum of 600 litres with probability density function 
\(\begin{cases} \begin{matrix} k & 200\le x\le 600 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\) 
Find
(i) the value of k
(ii) the distribution function
(iii) the probability that daily sales will fall between 300 litres and 500 litres?

If X is the random variable with probability density function f(x) given by,
\(f(x)=\begin{cases} \begin{matrix} x+1 & -1\le x<0 \end{matrix} \\ \begin{matrix} -x+1 & 0\le x<1 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\) 
then find
(i) the distribution function F(x)
(ii) P( -0.5 ≤X ≤ 0.5)

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)

A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer, indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be
(i) at least one defective item
(ii) exactly two defective items.

The mean and standard deviation of a binomial variate X are respectively 6 and 2.
Find
(i) the probability mass function
(ii) P(X = 3)
(iii) P(X\(\ge \)2).