Question

Problem 2.4 (10 points) Assume the sumber B of biosom on an apple tree is Poison dis tributed with paranner λ > 0 and "sppw that, indpratly hom all the others, each bloneom will yeld a fuit wih probablity pe 9 (a) Compute the probabilty mase fonction Pa of the sumber of apples A on the tree (b) Compate the conditlional probablityfmction of B oiven the sumber of apples A

Answer 1

Solution :

Given that

To the number B of blossoms on an apple tree is Poisson distributed with parameter $\lambda$

Soluton b The numb, of b lof son Bn, Passon (λ) probabit*i of apaA on Ta with B 2 istnbu6n

na lc n- K) ) n-K)

k! k t Grivun That зд PIA E) Now

v) n-E n- k)I n-t There fo