The cumulative distribution function of a random variable X is given by F(x) = 0; if x Find the probability density function of x and

1. The cumulative distribution function of a random variable X is given by

F(x)= 0; if x<= -

; if - < x <

1; if x >

Find the probability density function of x and P(- /2 < x < /2).

1. The length of time a person speaks over phone follows exponential distribution with mean 6. What is the probability that a person will talk for (i) more than 8 minutes (ii) between 4 and 8 minutes? If X is uniform random variable over the interval (a,b). Find the mean and variance of X.