GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

Hi,kindly reply with whole answers correct,accurate answers and step by step working.Do not skip step.Be very clear and mention about the formula for each step.Make sure the answers are correct and accurate. Be very organised with the working and systematic.Please explain to support and make it clear.

STA JANUARY 2018

QUESTION 5 a) The following probability distribution represents the number of children attending a mathematics course in a week. No. of children 2 3 5 6 P(X = X) 0.08 + a 0.44 0.16 + a 0.05 0.06 Find the value of a. (2 marks) Construct the cumulative distribution table for the number of children who attended the mathematics course in a week. (3 marks) Compute the probability that the number of children attending the mathematics course is at least 4 in a week. (3 marks) iv) Find E(X3 +4X-11). (4 marks) v) Find V(3X -5). (3 marks) b) A continuous random variable X has the following probability density function, /(x). 1( x ) =14 (1-x)(x - 3) : 15x53 : otherwise 1) Compute P(2 5 X s 3). (3 marks) ii) Find the expected value of X, E(X). (3 marks) ii) Find the variance of x, V(X). (4 marks)QUESTION 5 a) A private college organized an educational trip to a local university. There are 8 Statistics students and 10 Mathematics students at this college. If the trip can only be joined by 6 Statistics students and 7 Mathematics students, calculate the probability that the group of students selected for the trip. (4 marks) b) X and Y are independent events with P(X) = = and P(XUY) = = . Calculate P(Y). (5 marks) QUESTION 6 A milk producer company tested on their latest formula of M milk powder to prevent allergy for new born babies in a particular hospital. The probability for a baby feeding on milk powder in the hospital is 0.4. After giving the M milk powder to the babies, the probability for a baby getting an allergy is 0.3. Meanwhile, babies which have not been fed with M milk powder have a probability of 0.8 of getting an allergy. a) Construct a tree diagram to represent above information. (3 marks) b) Estimate the probability that a baby selected an allergy. (2 marks) c) If the baby gets an allergy, estimate the probability that M milk powder is given