If $Y _ { 1 } , Y _ { 2 } , \ldots Y _ { n }$

Essay

If $Y _ { 1 } , Y _ { 2 } , \ldots Y _ { n }$ are independent Poisson variables with common parameter $\theta$ then $\sum _ { i = 1 } ^ { n } Y _ { i }$ has also a Poisson distribution with parameter $\lambda$ = __________, where $\lambda$ denotes the expected number of defects per unit.