A mobile phone factory has a supply contract with a long-standing client. The client has to purchase c ∈ N mobile phones per month. In addition, the customer can order additional phones as required. The number of additional phones required can be modeled by a Poisson-distributed random variable X with parameter λ > 0.

 (a) Express the random variable Y = "total purchase in a given month” using X and c. 

(b) Determine the probability mass function of Y, depending on λ. 

(c) Determine P(Y ≤ 6) when λ = 6 and c= 4.