EXERCISE 11.4

EXERCISE . . For the random variable X with the given probability mass function or probability density function as below, find the mean and variance. (i) f x     , , , (ii) f x  , , (iii) f x ( ) =    otherwise (iv) f x ( ) = >      for otherwise . Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X. . If μ and σ are the mean and variance of the discrete random variable X , and E X and E X , find μ and σ . . Four fair coins are tossed once. Find the probability mass function, mean and variance for number of heads occurred. . A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is   elsewhere Obtain and interpret the expected value of the random variable X . . The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function  elsewhere Find the expected life of this electronic equipment. . The probability density function of the random variable X is given by xe   for for find the mean and variance of X . Probability Distributions