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 JUNE 2018

QUESTION 7 The random variable X has a probability distribution as given in the table below. X -2 -1 0 1 2 P(X=x) m 0.3 0.1 n 0.4 Given that E(X) = 0.25, calculate the following. a) Value of m and n. (5 marks) b) P(X > - 1). (2 marks) c) Variance of X, V(X). (4 marks) QUESTION 8 The probability density function of a continuous random variable is given by f( x ) = 27 ( /x2 -x3 ), OSX53 0, otherwise Calculate the following. a) Value of j. (4 marks) b) P( 2 s X s 3 ). (4 marks) c) The expected value of X, E(X). (4 marks) d) E(100 - 5X). (2 marks)QUESTION 3 a) In how many ways can the letters from the word FANTASTIC be arranged if 1) there is no restriction. (2 marks) ii) the word ends with "T". (2 marks) b) Given that P(M) = 0.6, P(M n N) = 0.4 and P(M U N) = 0.7, calculate i) P(N). (2 marks) ii) P(M'nN'). (2 marks) ill) P(N' | M'). (2 marks) c) From past experience, the probability that a new employee in a company who can perform well in his daily tasks is 0.85 if he has attended the in-house training and 0.36 if he has not attended the training. There is a 77% of new employees have attended the training. 1) Draw a tree diagram to represent the above situation. (3 marks) ii) Find the probability that a new employee can complete his works satisfactorily. (2 marks) ill) If the new employee can perform well in his daily tasks, what is the probability that he is untrained