Two factories manufacture orange juice. Factory 1 (resp. 2) manufactures juices of oranges whose quantity of sugar per b

[answerhappygod]

Two factories manufacture orange juice. Factory 1 (resp. 2)
manufactures juices of oranges whose quantity of sugar per bottle
X1 (resp. X2) follows an exponential law of parameter λ1 (resp. λ2)
These parameters verify λ1 <λ2 We have a bottle of juice of
orange which we know the amount of sugar it contains: q.
1. Show that E (X 1) = σ (X1) = λ ^ (- 1) then calculate the
distribution function of X1.
2- We try to test the hypothesis H 0 “the bottle comes from
factory 1” against the hypothesis H2 “The bottle comes from factory
2”. For this, we reject the hypothesis H0 when q is greater than or
equal to λ2
- Calculate the risk threshold for this test and its power.