This problem involves drawing three cards from a deck of cards. Assume that the deck contains 4 aces, 5 other face cards, and 9 non-face cards, and that you randomly draw 3 cards. A random variable Z is defined to be 3 times the number of aces plus 2 times the number of other face cards drawn. a. How many different values are possible for the random variable Z? b. Complete the probability density function. Be certain to list the values of Z in ascending order.
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!
This problem involves drawing three cards from a deck of cards. Assume that the deck contains 4 aces, 5 other face cards, and 9 non-face cards, and that you randomly draw 3 cards. A random variable Z is defined to be 3 times the number of aces plus 2 times the number of other face cards drawn.
a. How many different values are possible for the random variable Z?
b. Complete the probability density
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