Calculate the expected value E[X]. Calculate the variance VarX] and standard deviation o. If the stock cost $30.00, should you buy a share? Calculate the expected gain of ten shares of stock that cost $30 cach, that is, E[10X – 300].- Calculate the variance of the gain for ten shares. that is Var 10.X300.
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!
![### Problem Statement
2. Suppose that the random variable \( X \) represents the value of a share of stock after one year. Consider the following probability distribution:
| \( x \) | \( p(x) \) |
|:---------:|:-----------:|
| 0 | 0.74 |
| 50 | 0.12 |
| 100 | 0.09 |
| 200 | ? |
### Questions
a. Calculate the expected value \( E[X] \).
b. Calculate the variance \( \text{Var}[X] \) and standard deviation \( \sigma_X \).
c. If the stock costs $30.00, should you buy a share?
d. Calculate the expected gain of ten shares of stock that cost $30 each, that is, \( E[10X - 300] \).
e. Calculate the variance of the gain for ten shares, that is, \( \text{Var}[10X - 300] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ff7519c-27e7-46e8-b0a7-228922513039%2F6c8f3b40-3bd3-4c7d-a996-54a6c8b7d13f%2Fmhhrlek_processed.jpeg&w=3840&q=75)
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