15. | Binomial Probabilities: Coin Flip A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribu- tion and a calculator to compute the requested probability. Next, look up the probability in Table 3 of Appendix II and compare the table result with the computed result. (a) Find the probability of getting exactly three heads. (b) Find the probability of getting exactly two heads. (c) Find the probability of getting two or more heads. (d) Find the probability of getting exactly three tails.

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Please do not give solution in image formate thanku The textbook suggests 20-25% of the data used for forecasting should be used as the hold-out sample. Why might you want to use significantly more or significantly less data as your hold-out? What considerations go into determining hold-out length?

[Statistics] Use R or RStudio Context of the problem:Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in miles) and the percentage of fire damage were recorded. Here is the data set: Distance    Percent7.5    688.3    666.2    341.6    305.6    706    624.3    478.1    725.7    400.3    531.6    182.5    485.8    535.3    486.3    643.4    526.2    613.2    346.3    656.1    664.6    336.7    760.5    343.2    465.3    555    334.8    466.4    490.2    174.9    476.2    637.6    696.6    542.9    522.1    434.8    358.1    581.2    54.6    464    576.1    400.8    395.9    426.5    626.5    527.5    767.2    676.7    454.1    234    334.8    594…