Please solve questions 4- 5 - 7 - 8 . Thank you very much

4. Five thousand lottery tickets are sold for $1 each. One ticket will win $1,000, two tickets will win $500 each, and ten tickets will win $100 each. Let X denote the net gain from the purchase of a randomly selected ticket. a) Construct the probability distribution of X" b) Compute the expected value E(X) of X. Interpret its meaning. c) Compute the standard deviation o of X. 5. A waiter at the restaurant starts shifts with 0 dollars. Every guest gives him 5 or 10 dollars as a tip, with 5 dollar tip being 2 times more probable than 10 dollar one. One day the waiter served 4 guests. Calculate : a) probability of waiter getting less than 30 dollars in tip. b) expected sum of tips after 4 guests. 7. Given that the random variable X has density function: f ( x) = 2x, 0