6.3 The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distribution with A = 7 and B = 10. Find the probability that on a given day the amount of coffee dispensed by this machine will be (a) at most 8.8 liters;

The amount of milk (in litres) in a shop at the beginning of any day is a random amount 𝑋X from which a random amount 𝑌Y (in litres) is sold during that day. Assume that the joint density function of 𝑋X and 𝑌Y is given by𝑓𝑋𝑌(𝑥,𝑦)={1500≤𝑥≤10,0≤𝑦≤𝑥0otherwisef XY​ (x,y)={ 501​ 0​ 0≤x≤10,0≤y≤xotherwise​ .Find the probability that amount of milk left at the end of day is less than 4 litres. Write your answer correct to two decimal points.

A company responds to 80% of all enquiries within 2 working days. The firm received 8 enquiries today. What is the probability that all the 8 enquiries are responded within 2 working days?

On any given day, the probability that it will rain on the island of Sokatoa is estimated to be0.35 . The daily weather is observed on Sokatoa over the course of one month ( 28 consecutivedays).X is the random variable ‘number of days on which it rains’.a Find the probability that it rains on 14 days in total. (2)b Find the largest value of q such that ( ) 0.9P X q≤ < (3)c Given that it rains on 14 days in total, find the probability that it rains on seven days duringthe first two weeks and seven days during the second two weeks.

A jar has 13 candies where six of the candies are red, and seven candies are green. Imagine in a first draw, eight candies are randomly picked from the jar. We are interested in the number of green candies in that first draw. What is the distribution of X?Question 4Answera.X ~ B (7, 6, 8)b.X ~ H (7, 6, 8)c.X ~ G (7, 6, 8)

Consider X follows uniform distribution with A =-5 and B=7. Calculate P(−2.5≤X≤2.5) 𝑃 ( − 2.5 ≤ 𝑋 ≤ 2.5 ) a. 0.56 b. 0.24 c. 0.42 d. 0.30