ooks at an image consisting of two simple objects, O1 and O2, while linates of the focus of his gaze. When the subject looks at 0₁, the a racterised by a Gaussian probability density function 9₁ with mean robability density functiom g2 with mean 5 and variance 7 is used for ol bject looks at objects O₁ and O₂ are P(0₁) = 0.6 and P(O₂) = 0.4. late the posterior probability P(O₁|x = 1) nore probable that the subject was looking at object O₁ or O₂?

A catering service got hired to run the bar at a wedding with 100 guests. A wedding guest drinks on average 4 pints with variance of 0.9. i. Calculate how many pints the catering service approximately has to have in stock to be 95% sure that they can serve the demand.  ii. To be on the safe side the catering service decides to bring 430 pints. What is the approximate probability that those will suffice?

Please no written by hand solution

An electrochemical engineer has manufactured a new type of fuel cell (a type of battery)which has to undergo testing to prove its duration: the time it takes to go from fullycharged to completely uncharged, under a fixed nominal load. From the computational simulation models she has, the variance of the duration is σ2 = 4 h2 (hours squared)but she wants to estimate the mean duration time μ. To achieve this she is determinedto do the tests multiple times in independent but identical conditions. Can you findwhat is the smallest number of these tests that she has to do in order for her estimatedmean duration to be within ±0.2 h tolerance of the true mean with 95% certainty