Joe owns a coin that is either a fair coin or a two-headedcoin. Imelda believes that there is a 12chance that the coinis two-headed. She must guess what kind of coin Joe has. Ifshe guesses correctly, she pays Joe nothing, but if sheguesses incorrectly, she must pay Joe $2. Before guessing,she may pay 30¢ to see the result of a single coin toss (headsor tails). Determine how Imelda should minimize herexpected loss. Also determine EVSI and EVPI.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Joe owns a coin that is either a fair coin or a two-headed
coin. Imelda believes that there is a
1
2
chance that the coin
is two-headed. She must guess what kind of coin Joe has. If
she guesses correctly, she pays Joe nothing, but if she
guesses incorrectly, she must pay Joe $2. Before guessing,
she may pay 30¢ to see the result of a single coin toss (heads
or tails). Determine how Imelda should minimize her
expected loss. Also determine EVSI and EVPI.
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