Consider the experiment of tossing 7 balls into 5 bins with

Consider the experiment of tossing 7 balls into 5 bins, with each ball landing in each bin with equal probability independently. For each of the following random variables on this experiment, determine the named distribution and parameters that describes it. (5 points each) (a) X = the number of balls in bin 1. (b) Y = the number of balls in bin 1 plus the number of balls in bin 2. (c) Z1 = the bin where the first ball lands. (d) W = 0 if the first bin is empty, and 1 otherwise.

Solution

a)

X = number of balls in bin 1

X follows binomial distribution with parameters (7, 1/5)

b)

Y = number of balls in bin 1 + number of balls in bin2

=>
Y = X1 + X2

Y follows binomial distribution with parameters(7,1/5)

c)

Z1 = the bin where the first ball lands

Z1 follows poisson distribution with parameters(1/5)

d)

W is bernoulli distribution with parameter(1/5)