Q1

Let fX(a:) be the probability density function of the random variable X. f(m){%$ 03236; 0, otherwise. Find the mode of the distribution of X. l [The answer should be a number rounded to ve decimal places, don't use symbols such as %] The velocity v of an object of mass m = 5 Kg is a random variable with probability density function f(v) as given below. _ 1/23, 1.6 g '0 g 3.9 flu) { 0, otherwise. Find the mean value of the kinetic energy defined as y = 1/2 (mvz). l [The answer should be a number rounded to five decimal places, don't use symbols such as %] A computer system uses 5 digits numerical (from O to 9) passwords to provide access for resources, however, only one thousand passwords are valid. If a hacker enters a number (5 digits) at random, what is the probability that a randomly entered password will be valid? l [The answer should be a number rounded to ve decimal places, don't use symbols such as \"0]