2. Let the random variable X be the number of days that a certain patient needs to be in the hospital. Suppose X has the pmf f (x) = , x = 1, 2, 3, 4. If the patient is to receive $200 from an insurance company for each of the first two days in the hospital and $100 for each day after the first two days, what is the expected payment for the hospitalization? Translation: We have и (1). = 200 и (2) = 200 + 200 = 400 и (3) = 200 + 200+ 100 = 500 u (4) = 200 + 200 + 100 + 100 = 600 %3D What is E [X]?
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!
![2. Let the random variable X be the number of days that a certain patient needs to be in the
hospital. Suppose X has the pmf f (x)
from an insurance company for each of the first two days in the hospital and $100 for each day
after the first two days, what is the expected payment for the hospitalization? Translation:
5-a, x = 1,2, 3, 4. If the patient is to receive $200
10
We have
и (1)
= 200
u (2) = 200 + 200 = 400
u (3) = 200 + 200 + 100 = 500
и (4)
= 200 + 200 + 100 + 100 = 600
What is E [X]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36d93af9-1c60-4c54-a265-7600bbfc6b68%2Fc4c2ed95-1cf4-4129-b6f8-1976239fbca7%2Fuijwun_processed.jpeg&w=3840&q=75)
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