The discrete random variable X counts the number of heads that come up in 50 tosses of a fair coin. 1. Compute P(23 ≤ X ≤ 27) as precisely as you can. Note: compute probability for a binomial distribution using SageMath 2. Use Chebyshev’s Inequality to find a lower bound for P(23 ≤ X ≤ 27). How close is this lower bound to the actual value? 3. Use the standard normal distribution to approximate P(23 ≤ X ≤ 27). How close is this approximation to the actual value? 4. Toss an actual coin 50 times and record the sequence of heads and tails. a. Give the sequence of heads and tails that you recorded. How many heads came up in the 50 tosses you made? b. Do you think the outcome of your 50 tosses support the hypothesis that the coin is more-or-less fair?
The discrete random variable X counts the number of heads that come up in 50 tosses of a fair coin.
1. Compute P(23 ≤ X ≤ 27) as precisely as you can. Note: compute probability for a binomial distribution using SageMath
2. Use Chebyshev’s Inequality to find a lower bound for P(23 ≤ X ≤ 27). How close is this lower bound to the actual value?
3. Use the standard
4. Toss an actual coin 50 times and record the sequence of heads and tails.
a. Give the sequence of heads and tails that you recorded. How many heads came up in the 50 tosses you made?
b. Do you think the outcome of your 50 tosses support the hypothesis that the coin is more-or-less fair?
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