GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

IF YOU CANNOT TYPE,PLEASE PROVIDE NEAT AND CLEAR HANDWRITING.DO NOT GIVE BLUR AND CLUMSY WRITING.IT IS HARD FOR ME TO UNDERSTAND.

Kindly give accurate and correct answers.Kindly give step by step working.Do not skip steps. Mention and be very clear about the formula and conversion

.Then,explain to support and prove the working and answers.I do not really understand.I hope you can help me to understand.Explain how you get the answers and about each working.

Part 1

Problem 1 Let X be a random variable with PDF given by cm\" '3' 5 1 0 otherwise t\") = { a. Find the constant a. b. Find EX and Var(X]. c. Find P(X E % . \f1) The probability distribution function for a discrete random variable X is given by: (10-x) P(X = X) = forx = 0,1,2,3,4,5, k elsewhere a Find the value of k. b FindP(1