Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You initially don't know the probability of success in a single experiment. But you know that, if you continue to run the experiment several times, the variance of the number of experiments required for the first success is 2. What is the expected number of experiments required for the first success? [Hint: Try to determine the probability of success in a single experiment and recall the range of the values to which a probability must belong]
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!
Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You initially don't know the probability of success in a single experiment. But you know that, if you continue to run the experiment several times, the variance of the number of experiments required for the first success is 2. What is the expected number of experiments required for the first success? [Hint: Try to determine the probability of success in a single experiment and recall the
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