Please answer all of the questions #1-4 thoroughly with given explanations, thank you!

' .Question #1 v Ying Huang posted Aug 20, 2020 2:38 PM {If Subscribe What are the expected value, variance and standard deviation of a random variable? Given a probability distribution of random variable x: P(x=0)=0.2, P(x=1)=0.3, P(x=2)= 0.4, P(x=3)=0.1. Find the expected value and variance of x. Question#2 v Ying Huang posted Aug 20, 2020 2:38 PM 1% Subscribe What is a binomial experiment? What's the mean and standard deviation of a binomial distribution? Suppose 10% of the high school students are late for school.What is the probability that exactly 1 out of 5 students will be late for school? If we randomly select 50 students, what is the expected number of students who will be late for school? What is the standard deviation? > .Question #3 v Ying Huang posted Aug 20, 2020 2:39 PM {3 Subscribe The value of several items along with the probabilities that these items will be stolen over the next year are shown. Predict what the insurance company can expect to pay in claims on your policy. ls $100 a fair premium for this policy? Item Value Probability of being stolen laptop 2000 0.02 lphone 600 0.03 Trial Bike 400 0.01 Text Books 800 0.04 > .Question #4 v Ying Huang posted Aug 20, 2020 2:39 PM i? Subscribe One thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and cash prizes are to be awarded as follows: 1 prize of $100, 3 prizes of $50, and 5 prizes of $20. What is the expected value of this raffle if you buy 1 ticket