How to solve this set of question?

Homework 1 STATS 3011 Due:09/27/2020 11:59pm . All problems labeled R. problem must be done in R. . Please show all your work neatly. Points may be taken off your haphazard work. 1. R problem Load the dataset "hurricanes.csv" into R. Draw histograms for Pressure and Max Wind variables in the dataset. Are the distributions right skewed, left skewed or symmetric? Calculate the mean and standard deviation for Pressure and Max Wind. What are the r + 3sd bounds. 2. We have a dice. We are interested in the probability of rolling a 4 or a 5 or a 6. Calculate this probability. State what rule you used for this. 3. Suppose you toss a fair coin twice. What is the probability of getting 1 head and 1 tail? 1. Suppose you draw a card from a 52 card deck. This deck has 4 suits with 13 cards in each suit-spades, diamonds, hearts and clubs. What is the probability that the card you draw is a diamond? 5. Continuing from the above problem, in a standard deck hearts and diamonds are referred to as "Red" cards, while spades and clubs are referred to as "Black" cards. a. True or False: The probability of being dealt 3 red cards is ? = , ". If false, show how to get the correct probability. b. Let A=first card black and B-second card black. Are A, B independent? Explain why or why not. c. Answer part a. and b. if each card is returned to the deck after each draw. 6. Are people happy in their marriages? The table shows results from the 2008 General Social Survey for married adults classified by gender and level of happiness.Gender Very Happy Happy Not Happy Total Male 183 243 13 469 Female 215 247 38 500 Total 398 190 81 969 a. Estimate the probability that a married adult is very happy. b. Estimate the probability that a married adult is happy given- the gender is male, the gender is female. c. From the data provided, is being very happy and being male independent? 7. Suppose you pick out 4 cards from a deck of 52 cards. What is the probability you get 3 of a kind i.e. 3 cards with the same denomination (for example 3 aces)? What is the probability you get 4 of a kind? Which probability is smaller? 8. If A, B are independent events, prove that A", B" are also independent. 9. R problem Say you are tossing a coin and observing the outcome. You record 1 if the result is a head and 0 if it is a tail. Use the code "sample(c(0,1),1)" in R, to generate 10 such samples. Add them up. Do this entire exercise 10 times.(You may do this entire exercise in R or by hand) a. What is the mean of these 10 observations? b. What is the median? c. What is the mode