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Please help with question 10- 13. Please provide answers as well as explanations Question 10 A box contains three balls, numbered 1 through 3. Draw one and flip as many coins as the number on the ball. Collect as many dollars as coins that come up heads. Let X be your winnings. Determine the probability mass function for X, and then determine both E[X] and Var(X). Question 11 Cast a die 30 times. A. What is the probability you got either a 1 or 2 at least three times? B. What is the probability you got a 6 at least 8 times? Express your answer using the R function pbinom. C. What is the probability you got a 1, 2, 3, or 4 at least 10 times, but no more than 20 times? Express your answer using the R function pbinom. Question 12 Suppose a sample (X1,...,X45) of size 45 is drawn from a population X. If it is known that the mean of X is 10, and the variance is 20, determine the mean and variance of the distribution of the sample mean x ̃= 1/n ∑_(i=1)^n▒x_i Question 13 Suppose you cast a (six-sided) die 10 times, and toss a coin 20 times; all trials are independent. Get one point for each six and one point for each head. Let Xi be the number of points from the ith die toss, and let Yi be the number of points from the ith coin toss, determine both the expected number of total points and the variance of total points. 

          Please help with question 10- 13. Please provide answers as well as explanations
Question 10 
A box contains three balls, numbered 1 through 3. Draw one and flip as many coins as the number on the ball. Collect as many dollars as coins that come up heads. Let X be your winnings. Determine the probability mass function for X, and then determine both E[X] and Var(X). 
Question 11 
Cast a die 30 times. 
A. What is the probability you got either a 1 or 2 at least three times? 
B. What is the probability you got a 6 at least 8 times? Express your answer using the R function pbinom. 
C. What is the probability you got a 1, 2, 3, or 4 at least 10 times, but no more than 20 times? Express your answer using the R function pbinom. 
Question 12 
Suppose a sample (X1,...,X45) of size 45 is drawn from a population X. If it is known that the mean of X is 10, and the variance is 20, determine the mean and variance of the distribution of the sample mean x ̃=  1/n ∑_(i=1)^n▒x_i   
Question 13 
Suppose you cast a (six-sided) die 10 times, and toss a coin 20 times; all trials are independent. Get one point for each six and one point for each head. Let Xi be the number of points from the ith die toss, and let Yi be the number of points from the ith coin toss, determine both the expected number of total points and the variance of total points.
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Added by Paul C.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Please help with question 10- 13. Please provide answers as well as explanations Question 10 A box contains three balls, numbered 1 through 3. Draw one and flip as many coins as the number on the ball. Collect as many dollars as coins that come up heads. Let X be your winnings. Determine the probability mass function for X, and then determine both E[X] and Var(X). Question 11 Cast a die 30 times. A. What is the probability you got either a 1 or 2 at least three times? B. What is the probability you got a 6 at least 8 times? Express your answer using the R function pbinom. C. What is the probability you got a 1, 2, 3, or 4 at least 10 times, but no more than 20 times? Express your answer using the R function pbinom. Question 12 Suppose a sample (X1,...,X45) of size 45 is drawn from a population X. If it is known that the mean of X is 10, and the variance is 20, determine the mean and variance of the distribution of the sample mean x ̃= 1/n ∑_(i=1)^n▒x_i Question 13 Suppose you cast a (six-sided) die 10 times, and toss a coin 20 times; all trials are independent. Get one point for each six and one point for each head. Let Xi be the number of points from the ith die toss, and let Yi be the number of points from the ith coin toss, determine both the expected number of total points and the variance of total points.
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00:01 Okay, so here's the information we're given.
00:02 We're given that a 5kg ball is dropped from a height of 12 meters.
00:06 That's the first low column there.
00:08 And it's dropped onto a bar which is 8 kilograms and 4 meters in length.
00:12 And there's a second ball that's 5 kilograms that's resting on it.
00:16 And we want to know how high...
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