EXERCISE 11.2

EXERCISE . . Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred. . A six sided die is marked ‘ ’ on one face, ‘ ’ on two of its faces, and ‘ ’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find (i) the probability mass function (ii) the cumulative distribution function (iii) P X (iv) P X ≥ . Find the probability mass function and cumulative distribution function of number of girl child in families with children, assuming equal probabilities for boys and girls. . Suppose a discrete random variable can only take the values , , and . The probability mass function is defined by k , ,   for otherwise Find (i) the value of k (ii) cumulative distribution function (iii) P X ≥ . . The cumulative distribution function of a discrete random variable is given by F x          Find ( i ) the probability mass function ( ) ii iii P X and . A random variable X has the following probability mass function. k k k k k Find (i) the value of k (ii) P X (iii) P X < . The cumulative distribution function of a discrete random variable is given by F x ( ) = −∞< for for for for for for ≤ < ∞               Find (i) the probability mass function (ii) P X < and (iii) P X ≥ . - - Probability Distributions