Example 1: Functions of random variablesLetXbearandomvariablethattakesvaluefromOto9withegualprobability 1/10.· (a) Find the PMF of the random variable Y = X mod(3)1,4,72,5,80,3,6,9X012V4P3/103/10=2/510
Example 1: Functions of random variables • Let 𝑋 be a random variable that takes value from 0 to 9 with equal probability 1/10. • (a) Find the PMF of the random variable 𝑌 = 𝑋 𝑚𝑜𝑑(3). 6 X 0,3,6,9 1,4,7 2,5,8 Y 0 1 2 P 4 10 = 2/5 3/10 3/10
Example 1: Functions of random variablesLetXbearandomvariablethattakesvaluefromOto9withegualprobability 1/10.? (b) Find the PMF of the random variable Y = 5 mod(X + 1)0123456789X0121055555Y1250V2251/10P=1/5=1/5=1/2101010
Example 1: Functions of random variables • Let 𝑋 be a random variable that takes value from 0 to 9 with equal probability 1/10. • (b) Find the PMF of the random variable 𝑌 = 5 𝑚𝑜𝑑(𝑋 + 1). 7 X 0 1 2 3 4 5 6 7 8 9 Y 0 1 2 1 0 5 5 5 5 5 Y 0 1 2 5 P 2 10 = 1/5 2 10 = 1/5 1/10 5 10 = 1/2